Jan Willem Polderman

A state space approach to the problem of adaptive pole assignment

An adaptive pole-placement algorithm for the class of single-input/ single-output systems of ordern is proposed. The asymptotic properties of the algorithm do not depend on persistently exciting signals. Excitation is used only initially to avoid pole-zero cancellation of the parameter estimates. The main result is that the asymptotic behavior of the system equals the behavior we would have obtained on the basis of knowledge of the true system. This does not imply full identification of the desired control law, so we propose the descriptive termweak self-tuning.

Proper elimination of latent variables

We consider behaviors in which we distinguish two types of variables, manifest variables, the variables that are of interest to the user and latent variables, the variables that are introduced to obtain a first representation. The problem is to find a representation of the manifest behavior, that is, we want to eliminate the latent variables. If the original behavior can be represented by linear differential equations with constant coefficients, then under certain conditions the same is true for the manifest behavior. In this note we formulate and study these conditions. The results are illustrated by means of some examples. As an application we study behaviors in image representation.

Correction and simplification to “The order of a stabilizing regulator is sufficient a priori information for adaptive stabilization”

This note corrects a mistake in a paper by Martensson (1986). The main conclusion there (as reflected in the title) remains unchanged, only the construction of the `universal controller? has to be carried out slightly differently.

Asymptotic Dynamics in Adaptive Gain Control

It is well known that linear SISO systems that can be rendered passive through constant output feedback can be adaptively stabilized through a single gain adaptation law. We revisit the dynamical behavior of such systems and exhibit through a bifurcation analysis a rich variety of potential asymptotic dynamics, for which we provide a control theoretic interpretation. This in turn leads us to question the actual adaptive control question and solution approach.

Sequential continuous time adaptive control: a behavioral approach

We want to design a compensator for a behavior through an appropriate behavioral interconnection. The problem is that the behavior that we want to control is not known. All that is given is a desired interconnected behavior and the prior information that this desired behavior can indeed be achieved by means of regular interconnection. This problem calls for an adaptive flavored strategy. The strategy that we propose is as follows. Measurements are taken during successive time intervals of unit length. Each time a measurement is taken the most powerful unfalsified model of that measurement and the desired behavior is determined. Since this model contains the desired behavior it is possible to find additional constraints such that the desired behavior is achieved. Moreover these additional constraints can be chosen such that the corresponding interconnection is regular relative to the true unknown behavior. This regularity property makes it possible to invoke the additional constraints in the next time interval by incorporating a transient period. The new measurement therefore satisfies these additional constraints. The procedure is repeated for the new measurement and so on. The main result is that within a finite, though unknown, number of measurements the new measurements are constrained to the desired behavior.

High gain adaptive control revisited: first and second order case

Adaptive controllers based on high gain feedback suffer from lack of robustness with respect to bounded disturbances. Existing modifications prevent the feedback gain from drifting away, but at the same time introduce solutions that, even in the absence of disturbances, do not converge to zero. We investigate a further modification that maintains the robustness and rules out undesirable solutions when disturbances are not present. We restrict ourselves to first and second order systems.

Almost optimal adaptive LQ control: SISO case

Abstract. In this paper an almost optimal indirect adaptive controller for input/output dynamical systems is proposed. The control part of the adaptive control scheme is based on a modified LQ control law: by adding a time-varying gain to the certainty equivalent control law the conflict between identification and control is avoided.

A note on the structure of two subsets of the parameter space in adaptive control problems

We study the geometric structure of two subsets of the parameter space that are of interest in the context of adaptive LQ-control. The first set can be considered as the set of possible limit points of an adaptive control algorithm, whereas the second can be seen as the set of desirable limit points. Our main result is that these sets are

On the necessity of identifying the true parameter in adaptive LQ control

C^\omega

Parametrization of the Regular Equivalences of the Canonical Controller

-manifolds.