Eduardo D. Sontag

Control and Dynamical Systems (2008)

This paper provides further results about the equilinearization method of control design recently introduced by the author. A simplified derivation of the controller is provided, as well as a theorem...

Brian P. Ingalls, Eduardo D. Sontag

Consider the system with two output maps ˙x(t) = f(x(t), u(t)) (1) y(t) = h(x(t)), w(t) = g(x(t)), with state x ∈ R and controls u measurable essentially bounded functions into R m. Assume that...

www.molecularsystemsbiology.com Modular cell biology: retroactivity and insulation (2008)

Domitilla Del Vecchio, Er J Ninfa, Eduardo D Sontag

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon...

Molecular Systems Biology and Dynamics: An Introduction for non-Biologists (2008)

y (2008)

Network reconstruction based on steady-state data (2008)

Abstract The fundamental Filippov-Wa^zwski Relaxation Theorem states that the solution set of a initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same...

Passivity-based stability of interconnection (2008)

This paper discusses a theoretical method for the “reverse engineering ” of networks based solely on steady state (and quasi-steady state) data.

Eduardo D. Sontag, Murat Arcak

structures

www.molecularsystemsbiology.com Modular cell biology: retroactivity and insulation (2008)

Domitilla Del Vecchio, Er J Ninfa, Eduardo D Sontag

Modularity plays a fundamental role in the prediction of the behavior of a system from the behavior of its components, guaranteeing that the properties of individual components do not change upon...

Analytic aspects, local realizability, and i/o representations1 Yuan Wang (2008)

Recurrent perceptron classi ers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital ltering....

Eduardo D. Sontag, Hector J. Sussmann

Generating series and nonlinear systems:

with (2008)

output feedback design for linear systems

Sample Complexity for Learning Recurrent Perceptron Mappings y (2008)

Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in...

Bhaskar Dasgupta Z, Eduardo D. Sontag

stability, gap (2008)

We suggest that a very natural mathematical framework for the study of dissipation —in the sense of Willems, Moylan and Hill, and others — is that of indefinite quasimetric spaces. Several basic...

Angus Macintyre, Eduardo D. Sontag

This paper deals with analog circuits. It establishes the finiteness of VC dimension, teaching dimension, and several other measures of sample complexity which arise in learning theory. It also shows...

transduction and metabolic pathways: The (2008)

A Polynomial-Time Algorithm for Checking Equivalence Under Certain Semiring Congruences motivated by the State-space Isomorphism Problem for Hybrid Systems ∗ (2008)

Parameter estimation in models combining signal

On the structural monotonicity of chemical reaction (2008)

This paper presents a polynomial-time algorithm for equivalence under certain semiring congruences. These congruences arise when studying the isomorphism of state spaces for a class of hybrid...

David Angeli, Patrick De Leenheer, Eduardo D. Sontag

networks

GENERAL CLASSES OF CONTROL-LYAPUNOV FUNCTIONS (2008)

Abstract NEURAL NETS AS SYSTEMS MODELS AND CONTROLLERS ∗ (2008)

Abstract. The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finite-dimensional control systems and the existence of continuous...

KALMAN’S CONTROLLABILITY RANK CONDITION: FROM LINEAR TO NONLINEAR ∗ (2008)

This paper briefly surveys some recent results relevant to the suitability of “neural nets ” as models for dynamical systems as well as controllers for nonlinear plants. In particular, it touches...

On the existence of approximately coprime factorizations for retarded systems,” Systems and Control Letters 13(1989 (2008)

The notion of controllability was identified by Kalman as one of the central properties determining system behavior. His simple rank condition is ubiquitous in linear systems analysis. This article...

Eduardo D. Sontag, Yutaka Yamamoto

establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distribu-tions. The latter have been...

and (2008)

Abstract. This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous...

Thomas Natschläger, Wolfgang Maass, Eduardo D. Sontag, Anthony Zador

Experimental data show that biological synapses behave quite differently from the symbolic synapses in common artificial neural network models. Biological synapses are dynamic, i.e., their “weight...

Linear Systems With Sign-Observations (2008)

Renée Schwarzschild, Ee Schwarzschild, Eduardo D. Sontag

. This paper deals with systems that are obtained from linear time-invariant continuousor discrete-time devices followed by a function that just provides the sign of each output. Such systems appear...

x (2007)

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

This paper introduces and studies a new definition of the minimum-phase property for general smooth nonlinear control systems. The definition does not rely on a particular choice of coordinates in...

Proc. 1999 American Control Conf., pp. 1598--1602 1 On integral-input-to-state stabilization (2007)

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance...

z (2007)

a new de nition of the minimum-phase property for

z (2007)

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

A new denition of the minimum-phase property for

Minimum-Phase Nonlinear Systems: A New Definition (2007)

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

This paper introduces and studies a new denition of the minimum-phase property for general smooth nonlinear control systems. The denition does not rely on a particular choice of coordinates in which...

Finite Gain Stabilization of Discrete-Time Linear Systems Subject to Actuator Saturation (2007)

Xiangyu Bao Zongli, Xiangyu Bao, Zongli Lin, Eduardo D. Sontag

It is shown that, for neutrally stable discrete-time linear systems subject to actuator saturation, finite gain l p stabilization can be achieved by linear output feedback, for all p 2 (1; 1]. An...

Pole Shifting For Families Of Linear Systems Depending On At Most Three Parameters (2007)

General Classes Of Control-Lyapunov Functions (2007)

We prove that for any family of n-dimensional controllable linear systems, continuously parameterized by up to three parameters, and for any continuous selection of n eigenvalues (in complex...

Eduardo D. Sontag, H Ector, Héctor J. SUSSMANN

. The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finite-dimensional control systems and the existence of continuous control-Lyapunov...

A Polynomial-Time Algorithm for State Equivalence in Hybrid PL Systems (2007)

A Polynomial-Time Algorithm for State Equivalence in Hybrid PL Systems (2007)

The area of hybrid systems concerns issues of modeling, computation, and control for systems which combine discrete and continuous components. The subclass of piecewise linear (PL) systems provides...

Control-Lyapunov Functions For Time-Varying Set Stabilization (2007)

The area of hybrid systems concerns issues of modeling, computation, and control for systems which combine discrete and continuous components. The subclass of piecewise linear (PL) systems provides...

Kalman's Controllability Rank Condition: From Linear To Nonlinear (2007)

This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function...

Crowding effects promote coexistence in the chemostat, submitted (also DIMACS Tech report 2003-44; preliminary version entitled ‘A feedback perspective for chemostat models with crowding effects’ has appeared (2007)

The notion of controllability was identified by Kalman as one of the central properties determining system behavior. His simple rank condition is ubiquitous in linear systems analysis. This article...

Patrick De Leenheer, David Angeli, Eduardo D. Sontag

This paper deals with an almost-global stability result for a particular chemostat model. It deviates from the classical chemostat because crowding effects are taken into consideration. This model...

A relaxation theorem for differential inclusions with applications to stability properties (2007)

Patrick De Leenheer, David Angeli, Eduardo D. Sontag

The fundamental Filippov–Waˇzwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial...

with (2007)

feedback perspective for chemostat models

Abstract (2007)

A relaxation theorem for differential inclusions with applications to stability properties (2007)

Lemma 5 in [2] was incorrect. A correction is provided here. The error does not affect the rest of the results in the paper. 1 The Error and the Fix There is an error in the statement and the proof...

Measurement to error stability: a notion of partial detectability for nonlinear systems (2007)

The fundamental Filippov–Waˇzwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial...

North-Holland Publishing Company ON FINITELY ACCESSIBLE AND FINITELY OBSERVABLE RINGS (2007)

In previous work the notion of input to state stability (ISS) has been generalized to systems with outputs, yielding a number of useful concepts. When considering a system whose output is to be kept...

Eduardo D. Sontag, Communicalet S. Ellenberg

Two classes of rings which occur in linear system theory are introduced and compared. Characterizations of one of them are given in terms ot integral extensions and a Cayley- ttamitton type matrix...

On (2007)

Lars Grune, Eduardo D. Sontag, Fabian Wirth

equivalence of exponential and asymptotic stability under changes of variables

Produced as part of the ESPRIT Working Group in Neural and Computational Learning II, (2007)

Submitted to Systems and Control Letters 1 Universal construction of feedback laws achieving ISS and integral-ISS disturbance attenuation (2007)

For more information see the NeuroCOLT website

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

We study nonlinear systems with both control and disturbance inputs. The main problem addressed in the paper is design of state feedback control laws that render the closed-loop system...

;1 (2007)

Abstract: This paper studies the notion of output-input stability, which is a variant of the minimum-phase property for general smooth nonlinear control systems. In the spirit of the \input-to-state...

z (2007)

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

A new denition of the minimum-phase property for

Adaptive Control (2007)

Eduardo D. Sontag, Eduardo D. Sontag

1993 European Control Conference (short course on “Neural Nets for Control”). The first part places neurocontrol techniques in a general learning control framework. The second part of the report,...

Systems ConKK Letters 47 (2002) 167 -- 179 www.elsevier.com/locate/sysconT (2007)

Asymptotic Amplitudesan Cauchy, Eduardo D. Sontag

ThenepBGT of asymptotic amplitude forsignTzz an Cauchygain forinp# =output systems,an an asso iatedsmall-gain prin iple, areinpIzV ed. Theseon epts allow the onzzIBTp;#P of systems with multiple,an...

Pole Shifting For Families Of Linear Systems (2007)

Depending On At, Eduardo D. Sontag, Yuan Wang

We prove that for any family of n-dimensional controllable linear systems, continuously parameterized by up to three parameters, and for any continuous selection of n eigenvalues (in complex...

On the Existence of (2007)

Approximately Coprime Factorizations, Eduardo D. Sontag, Yutaka Yamamoto

This note establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distributions.

AN EXPLICIT CONSTRUCTION OF THE EQUILINEARIZATION CONTROLLER (2007)

Remarks On Input/output Linearization (2007)

This paper provides further results about the equilinearization method of control design recently introduced by the author. A simplified derivation of the controller is provided, as well as a theorem...

Abstract Available online at www.sciencedirect.com (2007)

In the context of realization theory, conditions are given for the possibility of simulating a given discrete time system, using immersion and/or feedback, by linear or state-affine systems.

MTNS Problem Book (2007)

Open Problems On, Vincent D. Blondel, Alexander Megretski, Roger Brockett, Jean-michel Coron, Miroslav Krstic, ...

this paper we consider the well-known Schur problem the solution of which satisfy in addition the extremal condition (z)w(z) min ; jzj < 1 (58.1) where w(z) and min are mxm matrices and min > 0...

in Neural and Computational Learning II, (2007)

Adaptation and regulation with signal detection implies internal model

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

For more information see the NeuroCOLT website

x (2007)

This paper introduces and studies a new denition of the minimum-phase property for general smooth nonlinear control systems. The denition does not rely on a particular choice of coordinates in which...

Capabilities and Training of Feedforward Nets (2007)

Modules and retroactivity: Theoretical framework, analysis, and design (2007)

This paper surveys recent work by the author on learning and representational capabilities of feedforward nets. The learning results show that, among two possible variants of the so-called...

Domitilla Del Vecchio, Alex Ninfa, Eduardo D. Sontag

In their influential paper [1], Hartwell et. al. argued for the recognition of functional “modules” as a critical level of biological organization, contending that modularity is a key feature...

distributed systems with a (2007)

Mihailo R. Jovanović, Murat Arcak, Eduardo D. Sontag

passivity-based approach to stability of spatially

J. Math. Biol. DOI 10.1007/s00285-007-0145-z Mathematical Biology On the number of steady states in a multiple futile cycle (2007)

Liming Wang, Eduardo D. Sontag

Abstract The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and...

Computational aspects of feedback in neural circuits (2007)

Wolfgang Maass, Prashant Joshi, Eduardo D. Sontag

It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with...

A Petri net approach to the study of persistence in chemical reaction networks (2006)

David Angeli, Patrick De Leenheer, Eduardo D. Sontag

Persistence is the property, for differential equations in R n, that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population...

J. Math. Biol. 52, 419–438 (2006) Mathematical Biology Digital Object Identifier (DOI): 10.1007/s00285-005-0344-4 (2006)

Patrick De, Leenheer Simon, A. Levin, Eduardo D. Sontag, Christopher A. Klausmeier

Abstract. We study a single species in a chemostat, limited by two nutrients, and separate nutrient uptake from growth. For a broad class of uptake and growth functions it is proved that a nontrivial...

Input to state stability: Basic concepts and results (2006)

Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles (2006)

The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic...

A Petri net approach to the study of persistence in (2006)

Strongly monotone systems of ordinary differential equations which have a certain translationinvariance property are shown to have the property that all projected solutions converge to a unique...

David Angeli, Patrick De Leenheer, Eduardo D. Sontag

chemical reaction networks

Passivity gains and the “secant condition” for stability (2006)

Principles of real-time computing with feedback applied to cortical microcircuit models (2006)

www.elsevier.com/locate/sysconle A generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems. The key is the introduction...

Wolfgang Maass, Prashant Joshi, Eduardo D. Sontag

What happens if one allows feedback from trained readouts? Figure 1: Expanding the “liquid computing model ” of [3] by allowing feedback from trained linear readouts. The circuit itself is a...

Nonlinear norm-observability notions and stability of switched systems (2005)

João P. Hespanha, Senior Member, Daniel Liberzon, Senior Member, David Angeli, Eduardo D. Sontag

Abstract—This paper proposes several definitions of “norm-observability” for nonlinear systems and explores relationships among them. These observability properties involve the existence of a...

Patrick De Leenheer, David Angeli, Eduardo D. Sontag

We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion...

Nonlinear norm-observability notions and stability of switched systems (2005)

João P. Hespanha, Senior Member, Daniel Liberzon, Senior Member, David Angeli, Eduardo D. Sontag

Abstract—This paper proposes several definitions of “norm-observability” for nonlinear systems and explores relationships among them. These observability properties involve the existence of a...

On predator-prey systems and small-gain theorems (2005)

Patrick De Leenheer, David Angeli, Eduardo D. Sontag

(Communicated by Sergei S. Pilyugin) Abstract. This paper deals with an almost global convergence result for Lotka-Volterra systems with predator-prey interactions. These systems can be written as...

On the stability of a model of testosterone dynamics (2004)

A Tutorial on Monotone Systems - With an Application to Chemical Reaction Networks (2004)

We prove the global asymptotic stability of a well-known delayed negativefeedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability...

Patrick De Leenheer, David Angeli, Eduardo D. Sontag

Monotone systems are dynamical systems for which the flow preserves a partial order. Some applications will be briefly reviewed in this paper. Much of the appeal of the class of monotone systems...

Monotone Systems Under Positive Feedback: Multistability and a Reduction Theorem (2004)

ARTICLE IN PRESS Systems & Control Letters ( ) – (2004)

For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a recent paper by Angeli and Sontag provided an approach to determining the location...

Digital Object Identifier (DOI): (2004)

www.elsevier.com/locate/sysconle Monotone systems under positive feedback: multistability and a reduction theorem

Optimal Length and Signal Amplification in Weakly Activated Signal Transduction Cascades (2004)

Abstract. We prove the global asymptotic stability of a well-known delayed negative-feedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish...

Madalena Chaves, Eduardo D. Sontag, Robert J. Dinerstein

Weakly activated signaling cascades can be modeled as linear systems. The input-to-output transfer function and the internal gain of a linear system provide natural measures for the propagation of...

An infinite-time relaxation theorem for differential inclusions (2003)

Brian Ingalls, Eduardo D. Sontag, Yuan Wang

Abstract. The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Waˇzewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion...

An example of a gas system which can be destabilized by an integrable perturbation (2003)

Eduardo D. Sontag, Mikhail Krichman

Abstract—A construction of a globally asymptotically stable time-invariant system which can be destabilized by some integrable perturbation is given. Besides its intrinsic interest, this serves to...

Monotone Control Systems (2003)

Nonlinear Observability Notions and Stability of Switched Systems (2003)

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to...

Joao P. Hespanha, David Angeli, Daniel Liberzon, Eduardo D. Sontag

This paper proposes several definitions of observability for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of...

A Remark on the Converging-Input Converging-State Property (2003)

Input-to-State Stability With Respect to Inputs and Their Derivatives (2003)

Suppose that an equilibrium is asymptotically stable when external inputs vanish. Then, every bounded trajectory which corresponds to a control which approaches zero and which lies in the domain of...

David Angeli, Eduardo D. Sontag, Y. Wang, Yuan Wang

INTRODUCTION A central question in control theory is how to formulate, for general non-linear systems, notions of robustness and stability with respect to exogenous input disturbances. The linear...

A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections (2002)

Brian Ingalls, Eduardo D. Sontag

Abstract A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form....

Output-input stability and minimum-phase nonlinear systems (2002)

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The denition of...

A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections (2002)

Eduardo D. Sontag, Brian Ingalls

A general input-to-state stability (ISS)-type small-gain result is presented. It specializes to a small-gainthallfor ISS operators, and it also recoversth classical statement for ISS systems in...

On Predator-Prey Systems and Small-Gain Theorems (2002)

Patrick De Leenheer, David Angeli, Eduardo D. Sontag

This paper deals with an almost global attractivity result for Lotka-Volterra systems with predator-prey interactions. These systems can be written as (negative) feedback systems. The subsystems of...

Monotone Control Systems (2002)

Characterizations of Detectability Notions in Terms of Discontinuous Dissipation Functions (2002)

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to...

Mikhail Krichman, Eduardo D. Sontag

This paper complements a recent result on smooth Lyapunov characterizations of IOSS. The utility of nonsmooth Lyapunov characterizations is illustrated by application to a well-known transistor...

Output-Input Stability and Minimum-Phase Nonlinear Systems (2002)

Daniel Liberzon, A. Stephen Morse, Eduardo D. Sontag

This paper introduces and studies the notion of output--input stability, which represents a variant of the minimum -phase property for general smooth nonlinear control systems. The definition of...

Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction (2001)

State-estimators for chemical reaction networks of Feinberg-Horn-Jackson zero-deficiency type (2001)

Abstract This paper deals with the theory of structure, stability, robustness, and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks. The...

Madalena Chaves, Eduardo D. Sontag

This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the...

Structure and Stability of Certain Chemical Networks and Applications to the Kinetic Proofreading Model of T-Cell Receptor Signal Transduction (2001)

Universal formulas for feedback stabilization with respect to Minkowski balls (2000)

This paper deals with the theory of structure, stability, robustness, and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks. The results...

Michael Malisoff, Eduardo D. Sontag

This note provides explicit algebraic stabilizing formulas for clf's when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a...

The ISS Philosophy as a Unifying Framework for Stability-Like Behavior (2000)

Analog Neural Nets with Gaussian (2000)

. The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical results...

Or Other Common, Wolfgang Maass, Eduardo D. Sontag

We consider recurrent analog neural nets where the output of each gate is subject to Gaussian noise, or any other common noise distribution that is nonzero on a sufficiently large part of the state...

Finite Gain Stabilization of Discrete-Time Linear Systems Subject to Actuator Saturation (2000)

Xiangyu Bao, Zongli Lin, Eduardo D. Sontag

It is shown that, for neutrally stable discrete-time linear systems subject to actuator saturation, finite gain l p stabilization can be achieved by linear output feedback, for all p 2 (1; 1]. An...

Neural systems as nonlinear filters (2000)

The ISS philosophy as a unifying framework for stability-like behavior (2000)

Experimental data show that biological synapses behave quite differently from the symbolic synapses in all common artificial neural network models. Biological synapses are dynamic, i.e., their...

www.elsevier.com/locate/sysconle Universal formulas for feedback stabilization with respect to Minkowski balls � (2000)

Abstract. The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical...

Michael Maliso, Eduardo D. Sontag

This note provides explicit algebraic stabilizing formulas for clf’s when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a...

Editors (1999)

Vincent D. Blondel, Alexander Megretski, Roger Brockett, Jean-michel Coron, Miroslav Krstic, Anders Rantzer, ...

Some of the problems appearing in this booklet will appear in a more extensive forthcoming book on open problems in systems theory. For more information about this future book, please consult the...

Forward completeness, unboundedness observability, and their Lyapunov characterizations (1999)

Analog neural nets with Gaussian or other common noise distribution cannot recognize arbitrary regular languages (1999)

Universit`a di Firenze, Via di Santa Marta 3,

Notions of Input to Output Stability (1999)

We consider recurrent analog neural nets where the output of each gate is subject to Gaussian noise, or any other common noise distribution that is nonzero on a large set. We show that many regular...

Eduardo D. Sontag, Y. Wang

This paper deals with concepts of output stability. Inspired in part by regulator

Daniel Liberzon Dept, Daniel Liberzon, Eduardo D. Sontag, Yuan Wang

This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance...

Input-Output-to-State Stability (1999)

Mikhail Krichman, Eduardo D. Sontag, Yuan Wang

This work explores Lyapunov characterizations of the input-output-to-state stability (ioss) property for nonlinear systems. The notion of ioss is a natural generalization of the standard...

On the equivalence between asymptotic and exponential stability, and between ISS and finite H infinity gain (1999)

Lars Grüne, Eduardo D. Sontag, Fabian Wirth

: We show that uniformly global asymptotic stability and input-to-state stability for a family of ordinary differential equations are equivalent to uniformly global exponential stability and a...

Asymptotic stability equals exponential stability, and ISS equals finite energy gain - if you twist your eyes (1999)

This paper continues the investigation of the recently introduced integral version of inputto -state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance...

Lars Grüne, Eduardo D. Sontag, Fabian R. Wirth

this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change...

New Characterizations of Input to State Stability (1999)

We present new characterizations of the Input to State Stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variations...

Universal formulas for CLF's with respect to Minkowski balls (1999)

This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance...

Minkowski Balls, Michael Malisoff, Eduardo D. Sontag

This note provides explicit, algebraic stabilizing formulas for clf's when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a...

This paper continues the investigation of the recently introduced integral version of inputto -state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance...

Control of Systems Without Drift via Generic Loops (1999)

This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance...

Clocks and insensitivity to small measurement errors (1999)

This paper proposes a simple numerical technique for the steering of arbitrary analytic systems with no drift. It is based on the generation of "nonsingular loops" which allow linearized...

Analog neural nets with Gaussian or other common noise distribution cannot recognize arbitrary regular languages (1999)

Abstract. This paper deals with the problem of stabilizing a system in the presence of small measurement errors. It is known that, for general stabilizable systems, there may be no possible...

Forward completeness, unboundedness observability, and their Lyapunov characterizations � (1999)

We consider recurrent analog neural nets where the output of each gate is subject to Gaussian noise, or any other common noise distribution that is nonzero on a sufficiently large part of the state...

Input-output-to-state stability (1999)

A nite-dimensional continuous-time system is forward complete if solutions exist globally, for positive time. This paper shows that forward completeness can be characterized in a necessary and su...

Mikhail Krichman, Eduardo D. Sontag, Yuan Wang

This work explores Lyapunov characterizations of the input-output-to-state stability (ioss) property for nonlinear systems. The notion of ioss is a natural generalization of the standard...

Brief Paper (1999)

Xiangyu Bao, Zongli Lin, Eduardo D. Sontag

Finite gain stabilization of discrete-time linear systems subject to actuator saturation �

Neural Systems as Nonlinear Filters (1998)

A Characterization of Integral Input to State Stability (1998)

Experimental data show that biological synapses behave quite differently from the symbolic synapses in all common artificial neuralnetwork models. Biological synapses are dynamic, i.e., their...

David Angeli, Eduardo D. Sontag, Yuan Wang

The notion of input to state stability (iss) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum...

Stability and Stabilization: Discontinuities and the Effect of Disturbances (1998)

VC Dimension of Neural Networks (1998)

this technicality.) In these terms, a stabilizing feedback is nothing else than a locally bounded map k : R! R such that k(0) = 0 and so that k is a section of ß on

A Polynomial-Time Algorithm for an Equivalence Problem which Arises in Hybrid Systems Theory (1998)

. This paper presents a brief introduction to Vapnik-Chervonenkis (VC) dimension, a quantity which characterizes the difficulty of distribution-independent learning. The paper establishes various...

Analog Neural Nets with Gaussian or other Common Noise Distributions cannot Recognize Arbitrary Regular Languages (1998)

Piecewise linear (PL) systems provide one systematic approach to discrete-time hybrid systems. They blend switching mechanisms with classical linear components, and model arbitrary interconnections...

Comments on Integral Variants of ISS (1998)

We consider recurrent analog neural nets where the output of each gate is subject to Gaussian noise, or any other common noise distribution that is nonzero on a large set. We show that many regular...

VC dimension of neural networks (1998)

Introduction We deal here with controlled systems of the general form x = f(x; u) ; (1) where f : R n \Theta R m ! R n is continuous, and locally Lipschitz on x for bounded u, and inputs u(\Delta) :...

Stability and stabilization: Discontinuities and the effect of disturbances (1998)

Abstract. This paper presents a brief introduction to Vapnik-Chervonenkis (VC) dimension, a quantity which characterizes the difficulty of distribution-independent learning. The paper establishes...

Vapnik-Chervonenkis dimension of recurrent neural networks (1998)

This expository paper deals with several questions related to stability and stabilization of nonlinear finite-dimensional continuous-time systems. The topics covered include a review of stability and...

Remarks on Universal Nonsingular Controls for Discrete-Time Systems (1997)

Abstract. Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications,...

Eduardo D. Sontag, Fabian R. Wirth

This paper is organized as follows. After defining the precise class of discretetime systems and stating the problem in Section 2 we prove the main results on universal nonsingular controls in...

A Lyapunov Characterization of Robust Stabilization (1997)

Yuri S. Ledyaev, Eduardo D. Sontag

One of the fundamental facts in control theory (Artstein's theorem) is the equivalence, for systems affine in controls, between continuous feedback stabilizability to an equilibrium and the...

Remarks on Universal Nonsingular Controls for Discrete-Time Systems (1997)

Eduardo D. Sontag, Fabian R. Wirth

For analytic discrete-time systems, it is shown that uniform forward accessibility implies the generic existence of universal nonsingular control sequences. A particular application is given by...

Global Stabilization of Linear Discrete-Time Systems with Bounded Feedback (1997)

Yudi Yang, Eduardo D. Sontag, Hector J. Sussmann

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time...

Vapnik-Chervonenkis Dimension of Recurrent Neural Networks (1997)

A Notion of Input to Output Stability (1997)

Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in...

Shattering All Sets of K Points in "general Position" Requires (k-1)/2 Parameters (1997)

. This paper deals with a notion of "input to output stability" (ios), which formalizes the idea that outputs depend in an "aymptotically stable" manner on inputs, while internal...

Global Stabilization of Linear Discrete-Time Systems with Bounded Feedback (1997)

For classes of concepts defined by certain classes of analytic functions depending on n parameters, there are nonempty open sets of samples of length 2n + 2 which cannot be shattered. A slighly...

Yudi Yang, Eduardo D. Sontag, Hector J. Sussmann

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time...

Vapnik-Chervonenkis Dimension of Recurrent Neural Networks (1997)

Neural networks with quadratic VC dimension (1997)

. Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in...

Comments on integral variants of ISS 1 (1997)

This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open...

Global stabilization of linear discrete-time systems with bounded feedback (1997)

This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L 2 stability, in much the same way that ISS generalizes L ∞...

Yudi Yang, Eduardo D. Sontag, Hector J. Sussmann

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time...

Output-to-State Stability and Detectability of Nonlinear Systems (1997)

A Smooth Converse Lyapunov Theorem for Robust Stability (1996)

Neural Networks with Quadratic VC Dimension (1996)

. This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical...

Sample Complexity for Learning Recurrent Perceptron Mappings (1996)

This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open...

Critical Points for Least-Squares Problems Involving Certain Analytic Functions, with Applications to Sigmoidal Nets (1996)

Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital...

Sample Complexity for Learning Recurrent Perceptron Mappings (1996)

This paper deals with nonlinear least-squares problems involving the fitting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability,...

Detectability Of Nonlinear Systems (1996)

Recurrent perceptron classifiers generalize the usual perceptron model. They correspond to linear transformations of input vectors obtained by means of "autoregressive movingaverage...

Sample Complexity for Learning Recurrent Perceptron Mappings (1996)

We propose a definition of detectability for nonlinear systems. This definition generalizes naturally the standard property in the linear case, and is consistent with the "input to state...

Vapnik-Chervonenkis Dimension of Recurrent Neural Networks (1996)

Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital...

Neural Networks with Quadratic VC Dimension (1996)

Most of the work on the Vapnik-Chervonenkis dimension of neural networks has been focused on feedforward networks. However, recurrent networks are also widely used in learning applications, in...

Output-to-State Stability and Detectability of Nonlinear Systems (1996)

This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open...

Interconnected Automata and Linear Systems: A Theoretical Framework in Discrete-Time (1996)

this paper is organized as follows. Section 2 provides the precise definition of

Interconnected automata and linear systems: A theoretical framework in discrete-time (1996)

. This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early...

Shattering all sets of k points in 'general position' requires (k \Gamma 1)=2 parameters", preprint (1996)

Abstract. This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the...

Sample complexity for learning recurrent perceptron mappings (1996)

For classes of concepts defined by certain classes of analytic functions depending on n parameters, there are nonempty open sets of samples of length 2n + 2 which cannot be shattered. A slighly...

A smooth converse Lyapunov theorem for robust stability (1996)

Recurrent perceptron classifiers generalize the usual perceptron model. They correspond to linear transformations of input vectors obtained by means of “autoregressive movingaverage schemes”, or...

Critical points for least-squares problems involving certain analytic functions, with applications to sigmoidal nets (1996)

Abstract. This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical...

Input to State Stabilizability for Parameterized Families of Systems (1995)

This paper deals with nonlinear least-squares problems involving the fitting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability,...

Input to State Stabilizability for Parameterized Families of Systems (1995)

This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control...

Neural Networks with Quadratic VC Dimension (1995)

This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control...

On Characterizations of the Input-to-State Stability Property (1995)

This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a long-standing open...

Sample Complexity for Learning Recurrent Perceptron Mappings (1995)

We show that the well-known Lyapunov sufficient condition for "input-to-state stability" is also necessary, settling positively an open question raised by several authors during the past...

Control of Systems Without Drift via Generic Loops (1995)

Recurrent perceptron classifiers generalize the classical perceptron model. They take into account those correlations and dependences among input coordinates which arise from linear digital...

Worst-Case Identification of Nonlinear Fading Memory Systems (1995)

. A simple numerical technique for path-planning is presented, which relies upon recent developments regarding the existence of universal nonsingular controls. It is based on the use of "generic...

Munther A. Dahleh, Eduardo D. Sontag, John N. Tsitsiklis

In this paper, the problem of asymptotic identification for fading memory systems in the presence of bounded noise is studied. For any experiment, the worst-case error is characterized in terms of...

Using Fourier-Neural Recurrent Networks to Fit Sequential Input/Output Data (1995)

Worst-Case Identification of Nonlinear Fading Memory Systems (1995)

This paper suggests the use of Fourier-type activation functions in fully recurrent neural networks. The main theoretical advantage is that, in principle, the problem of recovering internal...

Munther A. Dahleh, Eduardo D. Sontag, John N. Tsitsiklis

In this paper, the problem of asymptotic identification for fading memory systems in the presence of bounded noise is studied. For any experiment, the worst-case error is characterized in terms of...

On Characterizations of Input-to-State Stability with Respect to Compact Sets (1995)

Worst-Case Identification of Nonlinear Fading Memory Systems (1995)

Previous characterizations of iss-stability are shown to generalize without change to the case of stability with respect to sets. Some results on iss-stabilizability are mentioned as well.

Munther A. Dahleh, Eduardo D. Sontag, John N. Tsitsiklis

In this paper, the problem of asymptotic identification for a class of fading memory systems in the presence of bounded noise is studied. For any experiment, the worst-case error is characterized in...

On the Input-to-State Stability Property (1995)

Orders of Input/Output Differential Equations (1995)

The "input to state stability" (iss) property provides a natural framework in which to formulate notions of stability with respect to input perturbations. In this expository paper, we...

And State Space, Yuan Wang, Eduardo D. Sontag

This paper deals with the orders of input/output equations satisfied by nonlinear systems. Such equations represent differential (or difference, in the discrete-time case) relations between...

On Characterizations of the Input-to-State Stability Property (1995)

On characterizations of the input-to-state stability property (1995)

We show that the well-known Lyapunov sufficient condition for "input-to-state stability" is also necessary, settling positively an open question raised by several authors during the past...

On characterizations of input-to-state stability with respect to compact sets (1995)

The “input to state stability ” (iss) property provides a natural framework in which to formulate notions of stability with respect to input perturbations. In this expository paper, we review...

Tsitsiklis, “Worst-case identification of nonlinear fading memory systems (1995)

Abstract. Previous characterizations of iss-stability are shown to generalize without change to the case of stability with respect to sets. Some results on iss-stabilizability are mentioned as well....

Munther A. Dahleh, Eduardo D. Sontag, John N. Tsitsiklis

In this paper, the problem of asymptotic identification for fading memory systems in the presence of bounded noise is studied. For any experiment, the worst-case error is characterized in terms of...

On characterizations of the input-to-state stability property (1995)

Control-lyapunov universal formulas for restricted inputs (1995)

We show that the well-known Lyapunov sufficient condition for “input-to-state stability ” is also necessary, settling positively an open question raised by several authors during the past few...

Yuandan Lin, Eduardo D. Sontag

Keywords: Lyapunov functions, Artstein’s Theorem, Nonlinear stabilization We deal with the question of obtaining explicit feedback control laws that stabilize a nonlinear system, under the...

Tsitsiklis, “Worst-case identification of nonlinear fading memory systems (1995)

Munther A. Dahleh, Eduardo D. Sontag, John N. Tsitsiklis

This version was never published; the published version (in Automatica, 31, no. 3, March 1995) was very summarized. In this paper, the problem of asymptotic identification for a class of fading...

On the Computational Power of Neural Nets (1995)

Orders of input/output differential equations and state space dimensions (1995)

This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a “sigmoidal ” function to a linear...

Abstract. This paper deals with the orders of input/output equations satisfied by nonlinear systems. Such equations represent differential (or difference, in the discrete-time case) relations between...

Abstract (1995)

A general result on the stabilization of linear systems using bounded controls (1994)

This paper suggests the use of Fourier-type activation functions in fully recurrent neural networks. The main theoretical advantage is that, in principle, the problem of recovering internal...

Héctor J. Sussmann, Eduardo D. Sontag, Yudi Yang

We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on...

Analog Computation Via Neural Networks (1994)

A Smooth Converse Lyapunov Theorem for Robust Stability (1994)

We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to...

Orders of Input/Output Differential Equations and State Space Dimensions (1994)

. This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical...

A General Result on the Stabilization of Linear Systems Using Bounded Controls (1994)

This paper deals with the orders of input/output equations satisfied by nonlinear systems. Such equations represent differential (or difference, in the discrete-time case) relations between highorder...

Héctor J. Sussmann, Eduardo D. Sontag, Yudi Yang

We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on...

Recent Results on Lyapunov-theoretic Techniques for Nonlinear Stability (1994)

On the Intractability of Loading Neural Networks (1994)

This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems....

Bhaskar Dasgupta, Hava T. Siegelmann, Eduardo D. Sontag

Introduction Neural networks have been proposed as a tool for machine learning. In this role, a network is trained to recognize complex associations between inputs and outputs that were presented...

Analog Computation Via Neural Networks (1994)

Orders of Input/Output Differential Equations and State Space Dimensions (1994)

We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to...

A Comparison of the Computational Power of Sigmoid and Boolean Threshold Circuits (1994)

. This paper deals with the orders of input/output equations satisfied by nonlinear systems. Such equations represent differential (or difference, in the discretetime case) relations between...

Wolfgang Maass, Georg Schnitger, Eduardo D. Sontag

We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are...

Observability of Linear Systems with Saturated Outputs (1994)

Further Results on Controllability Properties of Discrete-Time Nonlinear Systems (1994)

In this paper, we present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function...

Analog computation via neural networks (1994)

Controllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity...

Observability of linear systems with saturated outputs (1994)

We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to...

Further results on controllability properties of discrete-time nonlinear systems (1994)

In this paper, we present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function...

A comparison of the computational power of sigmoid and Boolean threshold circuits (1994)

Controllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity...

Wolfgang Maass, Georg Schnitger, Eduardo D. Sontag

We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are...

State observability in recurrent neural networks (1994)

Francesca Albertini, Francesca Albertini, Eduardo D. Sontag, Eduardo D. Sontag

We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research.

Remarks on control lyapunov functions for discontinuous stabilizing feedback (1993)

G. A. Lafferriere, Eduardo D. Sontag

ABSTRACT We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth control-Lyapunov function exists. The resulting feedback is continuous at the origin and...

Finiteness Results for Sigmoidal "Neural" Networks (1993)

Angus Macintyre, Eduardo D. Sontag

) Angus Macintyre Mathematical Inst., University of Oxford Oxford OX1 3LB, England, UK E-mail: ajm@maths.ox.ac.uk Eduardo D. Sontag 3 Dept. of Mathematics, Rutgers University New Brunswick, NJ 08903...

Uniqueness Of Weights For Neural Networks (1993)

Francesca Albertini, Eduardo D. Sontag, Vincent Maillot

Introduction In most applications dealing with learning and pattern recognition, neural nets are employed as models whose parameters, or "weights," must be fit to training data. Gradient...

Neural Networks For Control (1993)

Discrete-Time Transitivity and Accessibility: Analytic Systems (1993)

This paper starts by placing neural net techniques in a general nonlinear control framework. After that, several basic theoretical results on networks are surveyed. 1 Introduction The field commonly...

Uniqueness Of Weights For Neural Networks (1993)

A basic open question for discrete-time nonlinear systems is that of determining when, in analogy with the classical continuous-time "positive form of Chow's Lemma," accessibility...

Francesca Albertini, Eduardo D. Sontag, Vincent Maillot

Introduction In most applications dealing with learning and pattern recognition, neural nets are employed as models whose parameters, or "weights," must be fit to training data. Gradient...

State Observability In Recurrent Neural Networks (1993)

Francesca Albertini, Francesca Albertini, Eduardo D. Sontag, Eduardo D. Sontag

We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research. Keywords: Recurrent neural networks, observability. This research was...

Some Topics in Neural Networks and Control (1993)

Eduardo D. Sontag, Eduardo D. Sontag

This report constitutes an expanded version of a presentation given by the author at the 1993 European Control Conference (short course on "Neural Nets for Control"). The first part places...

Remarks on Control Lyapunov Functions for Discontinuous Stabilizing Feedback (1993)

G. A. Lafferriere, Eduardo D. Sontag

We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth controlLyapunov function exists. The resulting feedback is continuous at the origin and smooth...

Uniqueness Of Weights For Recurrent Nets (1993)

Stabilization With Saturated Actuators, A Worked Example: F-8 Longitudinal Flight Control (1993)

this paper we prove the same result for arbitraryinitial state i/o maps. Moreover, we show that, for a generic subclass of these models, the minimality conditions needed in order for the results to...

Yudi Yang, Eduardo D. Sontag

Proc. 1993 IEEE Conf. on Aerospace Control Systems, Thousand Oaks, CA, May 1993, pp. 289-293 The authors and coworkers recently proved general theorems on the global stabilization of linear systems...

Uniqueness Of Weights For Recurrent Nets (1993)

For neural networks, function determines form (1993)

this paper we establish the same result for

Uniqueness of weights for recurrent nets (1993)

This paper shows that the weights of continuous-time feedback neural networks are uniquely identifiable from input/output measurements. Under very weak genericity assumptions, the following is true:...

Discrete-time transitivity and accessibility: analytic systems (1993)

We study recurrent neural networks evolving either in discrete or in continuous time. The dynamics of such systems can be described by a set of either difference or differential equations of the...

Uniqueness of weights for neural networks (1993)

A basic open question for discrete-time nonlinear systems is that of determining when, in analogy with the classical continuous-time “positive form of Chow’s Lemma,” accessibility follows from...

Francesca Albertini, Eduardo D. Sontag, Vincent Maillot

In most applications dealing with learning and pattern recognition, neural nets are employed as models whose parameters, or “weights, ” must be fit to training data. Gradient descent and other...

Remarks on control lyapunov functions for discontinuous stabilizing feedback (1993)

G. A. Lafferriere, Eduardo D. Sontag

We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth control-Lyapunov function exists. The resulting feedback is continuous at the origin and smooth...

Stabilization with saturated actuators, a worked example: F-8 longitudinal flight control (1993)

Yudi Yang, Eduardo D. Sontag

The authors and coworkers recently proved general theorems on the global stabilization of linear systems subject to control saturation. This paper develops in detail an explicit design for the...

Uniqueness of weights for recurrent nets (1993)

Neural networks for control (1993)

We study recurrent neural networks evolving either in discrete or in continuous time. The dynamics of such systems can be described by a set of either difference or differential equations of the...

Eduardo D. Sontag, Eduardo D. Sontag

This paper starts by placing neural net techniques in a general nonlinear control framework. After that, several basic theoretical results on networks are surveyed. 1

Adaptive Control (1993)

1993 European Control Conference (short course on “Neural Nets for Control”). The first part places neurocontrol techniques in a general learning control framework. The second part of the report,...

Neural Networks with Real Weights: Analog Computational Complexity (1992)

Hava T. Siegelmann, Hava T. Siegelmann, Eduardo D. Sontag, Eduardo D. Sontag

We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to...

For Neural Networks, Function Determines Form (1992)

Stabilization of Linear Systems With Bounded Controls (1992)

This paper shows that the weights of continuous-time feedback neural networks are uniquely identifiable from input/output measurements. Under very weak genericity assumptions, the following is true:...

Yudi Yang, H'ector J. Sussmann, Eduardo D. Sontag

. Linear systems with saturated controls can be smoothly stabilized as long as certain natural controllability and eigenvalue conditions hold, as shown in a previous paper by the authors....

Feedback Stabilization Using Two-Hidden-Layer Nets (1992)

Neural Nets As Systems Models And Controllers (1992)

This paper compares the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units. It is remarked that for...

For Neural Networks, Function Determines Form (1992)

This paper briefly surveys some recent results relevant to the suitability of "neural nets" as models for dynamical systems as well as controllers for nonlinear plants. In particular, it...

Francesca Albertini, Francesca Albertini, Eduardo D. Sontag, Eduardo D. Sontag

This paper shows that the weights of continuous-time feedback neural networks are uniquely identifiable from input/output measurements. Under very weak genericity assumptions, the following is true:...

Feedforward nets for interpolation and classification (1992)

Algebraic differential equations and rational control systems (1992)

This paper deals with single-hidden-layer feedforward nets, studying various aspects of classification power and interpolation capability. In particular, a worst-case analysis shows that direct input...

Systems Yuan Wang, Eduardo D. Sontag

An equivalence is shown between realizability of input/output operators by rational control systems and high order algebraic differential equations for input/output pairs. This generalizes, to...

Universal Nonsingular Controls (1992)

Feedback Stabilization Using Two-Hidden-Layer Nets (1992)

In this note we prove that, for analytic systems satisfying the strong accessibility rank condition, generic inputs produce trajectories along which the linearized system is controllable....

I/O Equations for Nonlinear Systems and Observation Spaces (1991)

This paper compares the representational capabilities of one hidden layer and two hidden layer nets consisting of feedforward interconnections of linear threshold units. It is remarked that for...

Some connections between chaotic dynamical systems and control systems (1991)

This paper studies various types of input/output representations for nonlinear continuous time systems. The algebraic and analytic i/o equations studied in previous papers by the authors are...

On The Computational Power Of Neural Nets (1991)

Abstract. This paper shows how to extend recent results of Colonius and Kliemann, regarding connections between chaos and controllability, from continuous to discrete time. The extension is...

Generating series and nonlinear systems: Analytic aspects, local realizability, and i/o representations (1991)

This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a "sigmoidal" function to a...

Yuan Wang Mathematics, Yuan Wang, Eduardo D. Sontag

This paper studies fundamental analytic properties of generating series for nonlinear control systems, and of the operators they define. It then applies the results obtained to the extension of...

Turing Computability With Neural Nets (1991)

On The Computational Power Of Neural Nets (1991)

. This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10 5 synchronously evolving...

Backpropagation Separates Where Perceptrons Do (1991)

This paper deals with the simulation of Turing machines by neural networks. Such networks are made up of interconnections of synchronously evolving processors, each of which updates its state...

Generating series and nonlinear systems: Analytic aspects, local realizability, and i/o representations (1991)

Feedforward nets with sigmoidal activation functions are often designed by minimizing a cost criterion. It has been pointed out before that this technique may be outperformed by the classical...

Input/Output and State-Space Stability (1991)

This paper studies fundamental analytic properties of generating series for nonlinear control systems, and of the operators they define. It then applies the results obtained to the extension of...

On The Computational Power Of Neural Nets (1991)

This paper first reviews various results relating state-space (Lyapunov) stabilization to notions of input/output or "bounded-input bounded-output" stabilization, and then provides...

Backpropagation separates where Perceptrons do (1991)

This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a "sigmoidal" function to a...

Turing Computability with Neural Nets (1991)

Feedforward nets with sigmoidal activation functions are often designed by minimizing a cost criterion. It has been pointed out before that this technique may be outperformed by the classical...

Input/output and state-space stability (1991)

Abstract. This paper shows the existence of a finite neural network, made up of sigmoidal neurons, which simulates a universal Turing machine. It is composed of less than 10 5 synchronously evolving...

A universal formula for stabilization with bounded controls (1991)

This paper first reviews various results relating state-space (Lyapunov) stabilization to notions of input/output or “bounded-input bounded-output ” stabilization, and then provides...

Some connections between chaotic dynamical systems and control systems (1991)

We provide a formula for a stabilizing feedback law using a bounded control, under the assumption that an appropriate control-Lyapunov function is known. Such a feedback, smooth away from the origin...

Mathematical Control Theory: Deterministic Finite Dimensional Systems (1990)

Abstract. This paper shows how to extend recent results of Colonius and Kliemann, regarding connections between chaos and controllability, from continuous to discrete time. The extension is...

Integrability of certain distributions associated to actions on manifolds and an introduction to Lie-algebraic control (1990)

The title of this book gives a very good description of its contents and style, although I might have added "Introduction to " at the beginning. The style is mathematical: precise,...

A Universal Formula For Stabilization With Bounded Controls (1990)

This file contains the original version of the following report: Integrability of certain distributions associated to actions on manifolds and an introduction to Lie-algebraic control

Yuandan Lin, Eduardo D. Sontag

We provide a formula for a stabilizing feedback law using a bounded control, under the assumption that an appropriate control-Lyapunov function is known. Such a feedback, smooth away from the origin...

Controllability Of Nonlinear Discrete Time Systems: A Lie-Algebraic Approach (1990)

B. Jakukczyk, Bronislaw Jakubczyk, Eduardo D. Sontag, Dim L

This paper presents a geometric study of controllability for discrete-time nonlinear systems. Various accessibility properties are characterized in terms of Lie algebras of vector fields. Some of the...

Nonlinear Output Feedback Design for Linear Systems With Saturating Controls (1990)

Feedback Stabilization of Nonlinear Systems (1990)

This paper shows the existence of (nonlinear) smooth dynamic feedback stabilizers for linear time invariant systems under input constraints, assuming only that open-loop asymptotic controllability...

Further facts about input to state stabilization (1990)

This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems. 1

Integrability of certain distributions associated to actions on manifolds and an introduction to Lie-algebraic control (1990)

Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to...

A "universal" Construction Of Artstein's Theorem On Nonlinear Stabilization (1989)

This file contains the original version of the following report: Integrability of certain distributions associated to actions on manifolds and an introduction to Lie-algebraic control

Feedback Stabilization Of Nonlinear Systems (1989)

This note presents an explicit proof of the theorem --due to Artstein-- which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. Moreover, the result is...

Some Connections Between Stabilization And Factorization (1989)

This paper surveys some well-known facts as well as some recent developments on the topic of stabilization of nonlinear systems. 1 Introduction In this paper we consider problems of local and global...

Further Facts About Input To State Stabilization (1989)

Coprime right fraction representations are obtained for nonlinear systems defined by differential equations, under assumptions of stabilizability and detectability. A result is also given on left...

Smooth Stabilization Implies Coprime Factorization (1989)

Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to...

Backpropagation Can Give Rise To Spurious Local Minima Even For Networks Without Hidden Layers (1989)

This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for...

Remarks On The Time-Optimal Control Of A Class Of Hamiltonian Systems (1989)

We give an example of a neural net without hidden layers and with a sigmoid transfer function, together with a training set of binary vectors, for which the sum of the squared errors, regarded as a...

Smooth Stabilization Implies Coprime Factorization (1989)

This paper introduces a subclass of Hamiltonian control systems motivated by mechanical models. Some problems of time-optimal control are studied, and results on singular trajectories are obtained. 1...

On Two Definitions Of Observation Spaces (1989)

This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for...

Yuan Wang Eduardo, Yuan Wang, Eduardo D. Sontag

This paper establishes the equality of the observation spaces defined by means of piecewise constant controls with those defined in terms of di#erentiable controls.

On Two Definitions Of Observation Spaces (1989)

Yuan Wang Eduardo, Yuan Wang, Eduardo D. Sontag

This paper establishes the equality of the observation spaces defined by means of piecewise constant controls with those defined in terms of differentiable controls.

Backpropagation can give rise to spurious local minima even for networks without hidden layers (1989)

Some Connections Between Stabilization and Factorization (1989)

We give an example of a neural net without hidden layers and with a sigmoid transfer function, together with a training set of binary vectors, for which the sum of the squared errors, regarded as a...

Remarks on the time-optimal control of a class of Hamiltonian systems (1989)

Coprime right fraction representations are obtained for nonlinear systems defined by differential equations, under assumptions of stabilizability and detectability. A result is also given on left...

A `universal' construction of Artstein's theorem on nonlinear stabilization (1989)

This paper introduces a subclass of Hamiltonian control systems motivated by mechanical models. Some problems of time-optimal control are studied, and results on singular trajectories are obtained. 1

Some Remarks On The Backpropogation Algorithm For Neural Net Learning (1988)

This note presents an explicit proof of the theorem –due to Artstein – which states that the existence of a smooth control-Lyapunov function implies smooth stabilizability. Moreover, the result...

Further Comments On The Stabilizability Of The Angular Velocity Of A Rigid Body (1988)

This report contains some remarks about the backpropagation method for neural net learning. We concentrate in particular in the study of local minima of error functions and the growth of weights...

Some remarks on the backpropogation algorithm for neural net learning, Rutgers Center for Systems and Control (1988)

We prove that the angular velocity equations can be smoothly stabilized with a single torque controller for bodies having an axis of symmetry. This complements a recent result of Aeyels and...

Further comments on the stabilizability of the angular velocity of a rigid body (1988)

This report contains some remarks about the backpropagation method for neural net learning. We concentrate in particular in the study of local minima of error functions and the growth of weights...

A Chow property for sampled bilinear systems," to appear (1987)

We prove that the angular velocity equations can be smoothly stabilized with a single torque controller for bodies having an axis of symmetry. This complements a recent result of Aeyels and...

Orbit Theorems and Sampling (1986)

An eigenvalue condition is given for the sampled positive-time accessibility of a class of nonlinear systems. This result generalizes a previous result of the

An introduction to the stabilization problem for parametrized families of linear systems (1985)

This paper proposes a notion of smooth action on a manifold, and establishes a general integrability result for certain associated distributions. As corollaries, various classical and new results on...

Real Addition And The Polynomial Hierarchy (1985)

New Results On Pole-Shifting For (1985)

The k-th alternation level of the theory of real numbers under addition and order is log-complete for the k-th level of the polynomial hierarchy.

Parametrized Families Of, Eduardo D. Sontag

New results are given on the pole-shifting problem for commutative rings, and these are then applied to conclude that rings of continuous, smooth, or real-analytic functions on a manifold X are PA...

Parametric stabilization is easy (1984)

An Algebraic Approach To Bounded Controllability Of Linear Systems (1984)

A polynomially parametrized family of continuous-time controllable linear systems is always stabilizable by polynomially parametrized feedback. 1. RESULTS Theorem 1. Let (A λ,B λ) be a pair of...

An algebraic approach to bounded controllability of linear systems (1984)

In this note we present an algebraic approach to the proof that a linear system with matrices (A,B) is null-controllable using bounded inputs iff it is null-controllable (with unbounded inputs) and...

Accessibility Under Sampling (1982)

In this note we present an algebraic approach to the proof that a linear system with matrices (A,B) is null-controllable using bounded inputs iff it is null-controllable (with unbounded inputs) and...

Eduardo D. Sontag, Hector J. Sussmann

This note addresses the following problem: Find conditions under which a continuous-time (nonlinear) system gives rise, under constant rate sampling, to a discrete-time system which satisfies the...

Accessibility under sampling (1982)

Eduardo D. Sontag, Hector J. Sussmann

This note addresses the following problem: Find conditions under which a continuous-time (nonlinear) system gives rise, under constant rate sampling, to a discrete-time system which satisfies the...

On the observability of polynomial systems, I: finite-time problems (1979)

Linear Systems and Noncommutative Rings (1976)

Abstract. Different notions of observability are compared for systems defined by polynomial difference equations. The main result states that, for systems having the standard property of...

Murat Arcak, Eduardo D. Sontag

This paper studies some problems appearing in the extension of the theory of linear dynamical systems to the case in which parameters are taken from noncommutative rings. Purely algebraic statements...

Abstract

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network...

Forward Completeness, Unboundedness Observability, and their Lyapunov Characterizations

Algebraic Differential Equations And Rational Control Systems

A finite-dimensional continuous-time system is forward complete if solutions exist globally, for positive time. This paper shows that forward completeness can be characterized in a necessary and...

Yuan Wang Mathematics, Yuan Wang, Eduardo D. Sontag

An equivalence is shown between realizability of input/output operators by rational control systems and high order algebraic differential equations for input/output pairs. This generalizes, to...

Algebraic Differential Equations And Rational Control Systems

Lyapunov Characterizations of Input to Output Stability

An equivalence is shown between realizability of input/output operators by rational control systems and high order algebraic differential equations for input/output pairs. This generalizes, to...

Forward Completeness, Unboundedness Observability, and their Lyapunov Characterizations

This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis...