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

In adaptive control problems one may drop the requirement of identifying the true system in order to simplify the problem of control. It will be shown that in the adaptive LQ control problem this does not at all lead to an easier problem

Adaptive LQ control: Conflict between identification and control

We consider one of the fundamental limitations of indirect adaptive control based on the minimization of a quadratic cost criterion and the certainty equivalence principle. We show that the interaction between (closed-loop) identification and optimal control is conflictive in the sense that almost all possible limits of the sequence of parameter estimates induce suboptimal behavior of the adaptively controlled system

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

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 system

Systems theoretic methods in decoding

In this paper we show how ideas based on system theoretic modeling of linear behaviors may be used for decoding of linear codes. In particular we show how Sudan's bivariate interpolation approach to list decoding of RS codes allows a system theoretic interpretation

Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

The topic of this paper is the analysis of stability for a class of switched linear systems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions

On the possible divergence of the projection algorithm

By means of an example, the authors show that the sequence of estimates generated by the projection algorithm does not always converge. The authors' construction shows that convergence is not automatically among the properties that can be derived without additional assumptions on the input sequenc

Reed-Solomon list decoding from a system-theoretic perspective

In this paper, the Sudan-Guruswami approach to list decoding of Reed-Solomon (RS) codes is cast in a system-theoretic framework. With the data, a set of trajectories or time series is associated which is then modeled as a so-called behavior. In this way, a connection is made with the behavioral approach to system theory. It is shown how a polynomial representation of the modeling behavior gives rise to the bivariate interpolating polynomials of the Sudan-Guruswami approach. The concept of "weighted row reduced" is introduced and used to achieve minimality. Two decoding methods are derived and a parametrization of all bivariate interpolating polynomials is given