Achim Ilchmann

Universal l-tracking for nonlinearly-perturbed systems in the presence of noise

Abstract For a class l of multivariable, nonlinearly-perturbed, linear, minimum-phase systems of relative degree one, with output measurement noise of Sobolev class W 1,∞ (absolutely continuous on compact intervals, and bounded with essentially bounded derivative), the following servomechanism problem is solved. Determine a l-universal adaptive strategy to control the output to track any reference signal in W 1,∞ , with tracking error asymptotic to a ball of arbitrary prescribed radius λ >0. The control strategy is simple and does not invoke an internal model principle.

Robustness of stability of time-varying linear systems

Abstract This paper introduces the concept of stability radius for time-varying linear systems. Invariance properties of the stability radius are analysed for the group of Bohl transformations. We also explore the relationship between the stability radius, the norm of a certain perturbation operator, and the solvability of a nonstandard differential Riccati equation. As an application we construct robust Lyapunov functions and show how they can be used to analyze robustness with respect to nonlinear perturbations.

High-gain adaptive l-tracking for nonlinear systems

Abstract 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 λ-tracking in the presence of output corrupted noise for a large class of reference signals and a large class of multivariable nonlinear ‘minimum-phase’ systems of relative degree one. These results are applied to a realistic chemical reactor, showing the practical usefulness of these control laws.

Tracking with Prescribed Transient Behavior for Nonlinear Systems of Known Relative Degree

Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class

Time-varying polynomial matrix systems

\Sigma_{\rho}

Tracking control: performance funnels and prescribed transient behaviour

of multi-input, multi-output dynamical systems, modelled by functional differential equations, affine in the control and satisfying the following structural assumptions: (i) arbitrary—but known—relative degree

PI-Funnel Control for Two Mass Systems

\rho \ge 1; (ii) the “high-frequency gain” is sign definite—but possibly of unknown sign. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains (as a prototype subclass) all finite-dimensional, linear,

Systems of Controlled Functional Differential Equations and Adaptive Tracking

m

On gain adaptation in adaptive control

-input,

Tracking control with prescribed transient behaviour for systems of known relative degree

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