A Local Second- and Third-order Maximum Principle (2008)
In this note we announce preliminary results obtained by applying the methodology of Sussmann [4, 5, 6, 7, 8] to the problem studied by Ledzewicz and Schättler (cf. [1, 2]), of deriving high-order...
fundamental solutions to linear systems (2008)
Mahesh G. Nerurkar, Héctor J. Sussmann
of ergodic cocycles that are
A Pontryagin Maximum Principle for systems of flows (2008)
We present a generalization of the Pontryagin Maximum Principle, in which the usual adjoint equation, which contains derivatives of the system vector fields with respect to the state, is replaced by...
fundamental solutions to linear systems (2008)
Mahesh G. Nerurkar, Héctor J. Sussmann
of ergodic cocycles that are
GENERAL CLASSES OF CONTROL-LYAPUNOV FUNCTIONS (2008)
Eduardo D. Sontag, Héctor J. Sussmann
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...
Needle Variations and Almost (2008)
Lower Semicontinuous, Differential Inclusions, Héctor J. Sussmann
A Pontryagin Maximum Principle for systems of flows (2008)
We present a generalization of the Pontryagin Maximum Principle, in which the usual adjoint equation, which contains derivatives of the system vector fields with respect to the state, is replaced by...
Some Versions of the Pontryagin Maximum Principle of Optimal Control Theory (2007)
ral completely rigorous versions of the "Pontryagin maximum principle." It is important that you should understand that, in spite of the differences in the technical assumptions, the basic...
A Nonsmooth Hybrid Maximum Principle (2007)
this paper we present a version of the maximum principle for nonsmooth hybrid optimal control problems, under weak regularity conditions. The class of hybrid problems to be considered is defined in
General Classes Of Control-Lyapunov Functions (2007)
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...
Differential-Geometric Methods: a Powerful Set of New Tools for Optimal Control (2007)
. Differential-geometric methods can and have been successfully used in control theory, not only to pose and solve new problems, but also to get new insights and prove new results about classical...
John Nohel, Héctor J. Sussmann
this paper, his only venture into control theory, Levinson solves the following basic problem of fundamental importance in the theory of linear control systems. Use IR
Abstract High-order open mapping theorems (2003)
The well-known finite-dimensional first-order open mapping theorem says that a continuous map with a finite-dimensional target is open at a point if its differential at that point exists and is...
Héctor J. Sussmann, Jan C. Willems
The purpose of this paper is to show that modern control theory, both in the form of the “classical ” ideas developed in the 1950s and 1960s, and in that of later, more recent methods such as the...
Set-valued differentials and the hybrid maximum principle (2000)
In recent years, it has become clear that most (smooth, nonsmooth, high-order, and hybrid) versions of the maximum principle (abbr. MP) for finite-dimensional, deterministic optimal control problems...
Output Feedback Adaptive Stabilization of a Second-Order Systems (2000)
Harshad S. Sane, Héctor J. Sussmann, Dennis S. Bernstein
We consider output feedback adaptive stabilization for second-order systems. The assumptions we make are standard, namely, that the system has relative degree two and the sign of the high frequency...
Continuous Dependence With Respect to the Input of Trajectories of Control-Affine Systems (1999)
Wensheng Liu, Héctor J. Sussmann
. We study the continuous dependence on the input of trajectories of control-affine systems belonging to the class C 0 (m) of all systems \Sigma of the form \Sigma : x = f 0 (x) + m X i=1 u i (t)f i...
Regular Synthesis and Sufficiency Conditions for Optimality (1998)
Benedetto Piccoli, Héctor J. Sussmann
We propose a definition of "regular synthesis," more general than those suggested by other authors such as Boltyanskii and Brunovsk'y, and an even more general notion of "regular...
Years Of Optimal Control: From The Brachystochrone To The Maximum Principle (1997)
Héctor J. Sussmann, Jan C. Willems
This paper was presented in the history session of the 35th Conference on Decision and Control in Kobe, Japan, on December 11, 1996. 300 years of optimal control 1 Optimal control was born in 1697...
The Markov-Dubins problem with angular acceleration control (1997)
We study a modified version of the well known MarkovDubins problem, in which the control is angular acceleration rather than angular velocity. We show that an optimal trajectory cannot contain a...
Lie Bracket Extensions And Averaging: The Single-Bracket Case (1997)
Single-bracket Case, Héctor J. Sussmann, Wensheng Liu
We explain a general approximation technique for nonholonomic systems by discussing in detail a special example, chosen so as to illustrate some of the technical aspects of the general construction....
A Cornucopia Of Four-Dimensional Abnormal Subriemannian Minimizers (1996)
. We study in detail the local optimality of abnormal sub-Riemannian extremals for a completely arbitrary sub-Riemannian structure on a four-dimensional manifold, associated to a two-dimensional...
Some Recent Results on the Maximum Principle of Optimal Control Theory (1996)
Introduction The maximum principle of optimal control theory (also known as the "Pontryagin maximum principle") was announced in the 1958 International Congress of Mathematicians, and...
Shortest paths for sub-Riemannian metrics on rank-two distributions (1995)
Wensheng Liu, Héctor J. Sussmann
We study length-minimizing arcs in sub-Riemannian manifolds (M;E;G) whose metric G is defined on a rank-two bracket-generating distribution E. It is well known that all length-minimizing arcs are...
Nonsmooth Control-Lyapunov Functions (1995)
Eduardo Sontag, Héctor J. Sussmann
It is shown that the existence of a continuous controlLyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finitedimensional control systems. The CLF...
A general result on the stabilization of linear systems using bounded controls (1994)
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...
A General Result on the Stabilization of Linear Systems Using Bounded Controls (1994)
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...
New Differential Geometric Methods in Nonholonomic Path Finding (1992)
We outline three approaches for nonholonomic path finding ---nilpotent approximation, highly oscillatory inputs and path deformation--- that are based on the use of the techniques of modern geometric...
On the Stabilizability of Multiple Integrators by Means of Bounded Feedback Controls (1991)
It is known that a linear system x = Ax + Bu can be stabilized by means of a smooth bounded control if and only if it has no eigenvalues with positive real part, and all the uncontrollable modes have...
Héctor J. Sussmann, Wensheng Liu
We describe sufficient conditions, extending earlier work by Kurzweil and Jarnik, for a sequence of inputs u j = (u j 1 ; : : : ; u j m ) 2 L 1 ([0; T ]; IR m ) to be such that, for every m-tuple (f...
Local Controllability And Motion Planning For Some Classes Of Systems With Drift (1991)
We explain how some recent results on the design of controls for nonoholomic systems without drift can be extended to some classes of sytems with drift. In particular, we show that a dynamic...
Backpropagation Separates Where Perceptrons Do (1991)
Eduardo D. Sontag, Héctor J. Sussmann
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...
Backpropagation separates where Perceptrons do (1991)
Eduardo D. Sontag, Héctor J. Sussmann
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...
Héctor J. Sussmann, Guoqing Tang
We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed...
Nonlinear Output Feedback Design for Linear Systems With Saturating Controls (1990)
Eduardo D. Sontag, Héctor J. Sussmann
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...
Eduardo D. Sontag, Héctor J. Sussmann
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...
Eduardo D. Sontag, Héctor J. Sussmann
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...
Further Comments On The Stabilizability Of The Angular Velocity Of A Rigid Body (1988)
Eduardo D. Sontag, Héctor J. Sussmann
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)
Eduardo D. Sontag, Héctor J. Sussmann
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...