Robustness of funnel control in the gap metric (2009)
Ilchmann, Achim, Müller, Markus
Preprint / Technische Universität Ilmenau, Institut für Mathematik; 09-19
Exponential stability of time-varying linear systems (2009)
Hill, Adrian T., Ilchmann, Achim
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 09-18
The Quasi-Weierstraß form for regular matrix pencils (2009)
Berger, Thomas, Ilchmann, Achim, Trenn, Stephan
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 09-21
Funnel control with saturation: nonlinear SISO systems (2009)
Hopfe, Norman, Ilchmann, Achim, Ryan, Eugene P.
Preprint / Technische Universität Ilmenau, Institut für Mathematik; 09-27
Funnel control with saturation: linear MIMO systems (2009)
Hopfe, Norman, Ilchmann, Achim, Ryan, Eugene P.
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 09-05
Indirect sampled-data control with sampling period adaptation (2008)
Ilchmann, Achim, Ke, Zhenqing, Logemann, Hartmut
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 08-22
Stability of positive linear Volterra integro-differential systems with delays (2008)
Ilchmann, Achim, Ngoc, Pham Huu Anh
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 08-21
Robust stabilization by linear output delay feedback (2008)
French, Mark, Ilchmann, Achim, Müller, Markus
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 08-16
Robust stabilization by linear output delay feedback (2008)
French, Mark, Ilchmann, Achim, Mueller, Markus
The main result establishes that if a controller $C$ (comprising of a linear feedback of the output and its \emph{derivatives}) globally stabilizes a (nonlinear) plant $P$, then global stabilization...
Performance funnels and tracking control (2008)
Ilchmann, Achim, Ryan, Eugene P.
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 08-13
On positivity and stability of linear time-varying Volterra equations (2008)
Ilchmann, Achim, Ngoc, Pham Huu Anh
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 08-05
Adaptive tracking with input constraints for exothermic (2007)
Achim Ilchmann, Mosalagae Thuto
chemical reactors
Maria do Ros'ario de Pinho (2007)
Weak maximum principle for optimal control problems with mixed constraints
Maria do Rosario de Pinho (2007)
Weak maximum principle for optimal control problems with mixed constraints
Adaptive Lambda-Tracking for a Class of Infinite-Dimensional Systems (2007)
Achim Ilchmann, Exeter Ex Qe, Hartmut Logemann, Claverton Down, Bath Ba Ay
: For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the...
Pneumatic cylinders: modelling and feedback force-control (2007)
Ilchmann, Achim, Sawodny, Oliver, Trenn, Stephan
In this paper, we model, analyse, and control an experimental set-up of a servo pneumatic cylinder. The dynamic behaviour of pneumatic actuator systems is dominant by non-linear functions. First, a...
Asymptotic tracking with prescribed transient behaviour for linear systems (2007)
Ilchmann, Achim, Ryan, Eugene P.
The problem of asymptotic tracking of reference signals is considered in the context of m-input, m-output linear systems (A,B,C) with the following structural properties: (i) CB is sign definite (but...
Robustness of λ-tracking in the gap metric (2007)
Ilchmann, Achim, Müller, Markus
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 07-13
Tracking with prescribed transient performance for hysteretic systems (2007)
Ilchmann, Achim, Logemann, Hartmut, Ryan, Eugene P.
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 07-01
PI-funnel control for two mass systems (2007)
Ilchmann, Achim, Schuster, Hans
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 07-02
Adaptive and non-adaptive control without identification: a survey (2006)
Ilchmann, Achim, Ryan, Eugene P.
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 06-10
Tracking with prescribed transient behaviour (2006)
Ilchmann, Achim, Ryan, Eugene P., Sangwin, Christopher J.
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 01-16
Tracking control: performance funnels and prescribed transient behaviour (2006)
Ilchmann, Achim, Ryan, Eugene P., Trenn, Stephan
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 04-8
A behavioural approach to timevarying linear systems (2006)
Ilchmann, Achim, Mehrmann, Volker
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 04-7
A behavioural approach to linear time-varying descriptor systems (2006)
Ilchmann, Achim, Mehrmann, Volker
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 04-11
Robust universal exponential adaptive stabilization in the presence of nonlinearities (2006)
Ilchmann, Achim, Owens, David H.
A unified approach to exponential adaptive stabilization via switching and gain adaptation is presented for a class of systems satisfying an integral inequality on input-output data. Two types of...
Adaptive sampled-data tracking for input constrained exothermic chemical reaction models (2006)
Ilchmann, Achim, Townley, Stuart, Thuto, Mosalagae
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 04-18
Characterization of the stability radius via bifurcation techniques (2006)
Robustness of stability of linear time-invariant systems using the relationship between the structured compex stability radius and a prametrized algebraic Riccato equation is analysed. Our approach...
Tracking with prescribed transient behaviour for nonlinear systems of known relative degree (2006)
Ilchmann, Achim, Ryan, Eugene P., Townsend, Philip
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-14
Algebraic theory of time-varying linear systems: a survey (2006)
The development of the algebraic theory of time-varying linear systems is described. The class of systems considered consists of differential-algebraic equation in kernel presentation. This class...
Stabilization of linear systems by dynamic high-gain rotation (2006)
Crauel, Hans, Damm, Tobias, Ilchmann, Achim
We discuss stabilisation of linear systems by dynamic high-gainrotation. The existence of stabilizing rotations is established forsystems with negative trace, and an adaptive method to choose...
Stabilization of linear systems by rotation (2006)
Crauel, Hans, Damm, Tobias, Ilchmann, Achim
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-18
Time-varying linear systems : relative degree and normal form (2006)
Ilchmann, Achim, Müller, Markus
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-15
Non-identifier-based high-gain adaptive control (2006)
Zugl.: Hamburg, Univ., FB Mathematik, Habil.-Schr., 1993
Tracking control with prescribed transient behaviour for systems of known relative degree (2006)
Ilchmann, Achim, Ryan, Eugene P., Townsend, Philip
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-02
On stability of linear time-varying second-order differential equations (2006)
Duc, Luu Hoang, Ilchmann, Achim, Siegmund, Stefan, Taraba, Peter
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-03
Robustness in the graph topology of a common adaptive controller (2006)
French, Mark, Ilchmann, Achim, Ryan, Eugene P.
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-10
Pneumatic cylinders : modelling and feedback force-control (2006)
Ilchmann, Achim, Sawodny, Oliver, Trenn, Stephan
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-05
Asymptotic tracking with prescribed transient behaviour for linear systems (2006)
Ilchmann, Achim, Ryan, Eugene P.
Preprint / Technische Universität Ilmenau, Institut für Mathematik ; 05-06
A behavioural approach to time-varying linear systems, Part 1: General theory (2006)
Ilchmann, Achim, Mehrmann, Volker
We develop a behavioral approach to linear, time-varying, differential-algebraic systems. The analysis is "almost everywhere" in the sense that the statements hold on R \ T, where T is a discrete...
A behavioural approach to time-varying linear systems, Part 2: Descriptor systems (2006)
Ilchmann, Achim, Mehrmann, Volker
In the sequel to [A. Ilchmann and V. Mehrmann, SIAM J. Control Optim., 44 (2005), pp. 1725–1747], we discuss a behavioral approach for linear, time-varying, differential algebraic (descriptor)...
Continuous time-varying scalar systems : a behavioural approach (2005)
Ilchmann, Achim, Kuang, Yan, Kuijper, Margreet, Zhang, Cishen
Bullinger, Eric, Ilchmann, Achim, Allgöwer, Frank
In this paper we present an adaptive high-gain observer-based controller for linear, minimum-phase systems with known relative degree larger than one and known sign of the high-frequency gain. The...
A simple adaptive observer for nonlinear systems (2005)
Bullinger, Eric, Ilchmann, Achim, Allgöwer, Frank
In this note we present a high-gain observer for nonlinear uniformly observable SISO systems for which the high-gain parameter is determined adaptively on-line. The adaptation scheme is simple and...
Adaptive regulation of a biogas tower reactor (2005)
Ilchmann, Achim, Pahl, M., Lunze, Jan
A simple adaptive high-gain regulator is designed for a nonlinear multivariable Biogas Tower Reactor. The controller achieves tracking of the constant reference signals within a prespecified...
Adaptive high-gain fast sampling P-control (2005)
Ilchmann, Achim, Townley, Stuart
In this paper we show that well-known high-gain universal adaptive P-controllers can be implemented digitally, via adaptive sampling, provided that the length of the sampling interval increases...
Stabilizability of systems with exponential dichotomy (2005)
In this paper we introduce the concept of controllability into a closed subspace for time-varying linear systems. Various characterizations are given and the dual relation is discussed. This concept...
Adaptive λ-[lambda]-tracking for a class of infinite-dimensional systems (2005)
Ilchmann, Achim, Logemann, Hartmut
For a class of high-gain stabilizable multivariable linear infinite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the...
Adaptive high-gain λ-[lambda]-tracking with variable sampling rate (2005)
Ilchmann, Achim, Townley, Stuart
It is well known that proportional output feedback control can stabilize any relative-degree one, minimum-phase system if the sign of the feedback is correct and the proportional gain is high enough....
Contributions To Time-Varying Linear Control Systems (2005)
Zugl.: Bremen, Univ., Diss., 1987
λ-[lambda]-tracking for exothermic chemical reactions with saturating inputs (2005)
Ilchmann, Achim, Thuto, Mosalagae, Townley, Stuart
We consider adaptive regulation of the temperature for exothermic chemical reactors. These reactors may exhibit multiple steady states, and the relevant operating point could be an unstable open-loop...
On optimality conditions for optimal control problems with mixed constraints (2005)
An optimal control problem for time-varying, nonlinear differential equations with state-dependent control constraints is considered, the data may be nonsmooth. A weak maximum principle for problems...
Adaptive tracking for systems described by functional differential equations (2005)
Ilchmann, Achim, Ryan, Eugene P., Sangwin, Christopher J.
An adaptive servomechanism is developed for practical tracking (with prespecified asymptotic accuracy), by the system output, of any admissible reference signal (viz. absolutely continuous and...
High-gain adaptive stabilization of multivariable linear systems - revisited (2005)
Ilchmann, Achim, Logemann, Hartmut
We consider the class of multi-input multi-output, finite dimensional, state space systems of the form x=Ax+Bu. Y, where the state dimension is unknown, the system is minumum phase, and it is known...
Exponential Stabilization using Piecewise Constant Gain Adaptation (2005)
Owens, David H., Ilchmann, Achim
An adaptive stabilizer for a class of single-input-single-output (SISO) minimum phase systems with known sign is introduced. It extends the work of J.C. Willems and C.I. Byrnes (1984) but uses a...
Modelling of general biotechnological processes (2005)
Ilchmann, Achim, Weirig, Marie-France
A general biotechnological process is modelled by a finite dimensional ordinary differential equation. The stoichiometry is only modelled qualitatively. It is shown that the usual biochemically...
Oxygen Diffusion in Tissue Preparations with Michaelis-Menten Kinetics (2005)
Bassom, Andrew P., Ilchmann, Achim, Voß, Heinrich
A model is introduced for the oxygen consumption in thin vital tissue preparation. The steady uptake kinetics is modelled by a MichaelisMenten form and for this case it proved that the resulting...
Adaptive λ-[lambda]-tracking control of activated sludge processes (2005)
Ilchmann, Achim, Georgieva, Petia
An adaptive controller for activated sludge processes is introduced. The control objective is to keep, in the presence of input constraints, the concentration of the biomass proportional to the...
Universal λ-[lambda]-tracking for nonlinearly-perturbed systems in the presence of noise (2005)
Ilchmann, Achim, Ryan, Eugene P.
For a class l of multivariable, nonlinearly-perturbed, linear, minimum-phase systems of relative degree one, with output measurement noise of Sobolev class W1,00 (absolutely continuous on compact...
Asymptotic Dynamics in Adaptive Gain Control (2005)
Ilchmann, Achim, Mareels, Iven M. Y., Van Gils, S., Poldermann, Jan Willem
Robust Adaptive Stabilization of Discrete-time First-order Systems (2005)
An algorithm for the adaptive stabilization of single-input single-output time-varying first-order discrete-time systems is presented. Only the knowledge of the sign of the feedback gain and an upper...
High-gain adaptive λ-[lambda]-tracking for nonlinear systems (2005)
Ilchmann, Achim, Allgöwer, Frank, Ashman, Jon
It is shown that a simple modification (introducing a dead zone in the adaptation law) of the known adaptive high-gain control strategy u(t) = -k(t)y(t), k(t) = ||y(t)||2 yields lambda-tracking in...
Existence and learning of oscillations in recurrent neural networks (2005)
Townley, Stuart, Ilchmann, Achim, Weiss, M. G., Mcclements, W., Ruiz, A. C., Owens, David H., ...
We study a particular class of n-node recurrent neural networks (RNNs). In the 3-node case we use monotone dynamical systems theory to show, for a well-defined set of parameters, that, generically,...
High-gain robust adaptive controllers for multivariable systems (2005)
Ilchmann, Achim, Owens, David H., Prätzel-Wolters, Dieter
This paper extends the switching free high-gain stabilizing adaptive control rules of Byrnes and Willems to a wide class of adaptive schemes capable of tolerating nonlinear state feedback...
On tracking and disturbance rejection by adaptive control (2005)
Ilchmann, Achim, Ryan, Eugene P.
For linear minimum-phase relative-degree-one systems subject to disturbances and nonlinear perturbations, results pertaining to disturbance rejection and adaptive tracking of constant reference...
Adaptive stabilization with exponential decay (2005)
Ilchmann, Achim, Owens, David H.
Adaptive high gain stabilizers for classes of linear time-invariant state space systems are presented. The classes cover multi-input - multi-output systems where the state dimension is not known....
Simple adaptive stabilization of high-gain stabilizable systems (2005)
Ilchmann, Achim, Townley, Stuart
It is shown that the simple adaptive feedback strategy u(t)=1ln k(t) cos1/ln(t).k(t)=y(y)² is a universal adaptive stabilizer for the class of single-input, single-output, finite-dimensional, linear...
Systems of controlled functional differential equations and adaptive tracking (2005)
Ilchmann, Achim, Ryan, Eugene P., Sangwin, Christopher J.
An adaptive servomechanism is developed in the context of the problem of approximate or practical tracking (with prescribed asymptotic accuracy), by the system output, of any admissible reference...
Input constrained adaptive tracking with applications to exothermic chemical reactions models (2005)
Ilchmann, Achim, Thuto, Mosalagae, Townley, Stuart
"We consider input constrained adaptive output feedback control for a class of nonlinear systems which are prototype models for controlled exothermic chemical reactions. Our objective is set-point...
An adaptive servomechanism for a class of infinite-dimensional systems (2005)
Ilchmann, Achim, Logemann, Hartmut
A universal adaptive controller is constructed that achieves asymptotic tracking of a given class of reference signals and asymptotic rejection of a prescribed set of disturbance signals for a class...
Tracking with prescribed transient behaviour (2005)
Ilchmann, Achim, Ryan, Eugene P., Sangwin, Christopher J.
Universal tracking control is investigated in the context of a class S of M-input, M-output dynamical systems modelled by functional differential equations. The class of systems encompasses a wide...
Adaptive sampling control of high-gain stabilizable systems (2005)
Ilchmann, Achim, Townley, Stuart
It is well known that proportional output feedback control can stabilize any relative-degree one, minimum-phase system if the sign of the feedback is correct and the proportional gain is high enough....
Time-varying linear systems: relative degree and normal form (2005)
We define the relative degree of time-varying linear systems, show that it coincides with Isidori’s and with Liberzon/Morse/Sontag’s definition if the system is understood as a timeinvariant...
Existence and Learning of Oscillations in Recurrent Neural Networks (2000)
Townley, Stuart, Ilchmann, Achim, Weiß, Martin G., McClements, Warren, Ruiz, Antonio C., Owens, David H., ...
In this paper we study a particular class of$n$-node recurrent neural networks (RNNs).In the $3$-node case we use monotone dynamical systems theory to show,for a well-defined set of parameters,...
A simple adaptive observer for nonlinear systems (1998)
Bullinger, Eric, Ilchmann, Achim, Allgöwer, Frank
Proc. of the IFAC Nonlinear Control Systems Design, NOLCOS98
Non-Identifier-Based Adaptive Control of Dynamical Systems: A Survey (1991)
In adaptive control, the objective is to provide a single controller (consisting of a feedback law and a parameter adaptation law) which can control each system belonging to a certain class of...
Threshold Switching Functions in High-Gain Adaptive Control (1991)
ILCHMANN, ACHIM, OWENS, DAVID H.
Adaptive stabilizers for the class of m-input m-output minimum phase systems $$\dot{x}=Ax+Bu,\hbox{ \hspace{0.17em} }\hbox{ \hspace{0.17em} }\hbox{ \hspace{0.17em} }y=Cz$$ with unknown state...
Exponential Stabilization using Nondifferential Gain Adaptation (1990)
ILCHMANN, ACHIM, OWENS, DAVID H.
A new type of adaptive high-gain stabilizer for classes of linear time-invariant state-space systems is presented. The classes cover multi-input multi-output systems where the state dimension is not...
Time-Varying Linear Control Systems: A Geometric Approach (1989)
The concept of [A, B]-invariance for time-varying (not necessarily continuous) linear systems is introduced. A natural approach via time-varying subspaces is given. A disturbance decoupling and a...
Contributions to time-varying Linear Control Systems / (1987)
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