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© 1987

Stabilization of Control Systems

Book

Part of the Applications of Mathematics book series (SMAP, volume 20)

Table of contents

  1. Front Matter
    Pages i-xii
  2. O. Hijab
    Pages 1-20
  3. O. Hijab
    Pages 21-42
  4. O. Hijab
    Pages 43-63
  5. O. Hijab
    Pages 64-83
  6. O. Hijab
    Pages 84-102
  7. Back Matter
    Pages 103-129

About this book

Introduction

The problem of controlling or stabilizing a system of differential equa­ tions in the presence of random disturbances is intuitively appealing and has been a motivating force behind a wide variety of results grouped loosely together under the heading of "Stochastic Control." This book is concerned with a special instance of this general problem, the "Adaptive LQ Regulator," which is a stochastic control problem of partially observed type that can, in certain cases, be solved explicitly. We first describe this problem, as it is the focal point for the entire book, and then describe the contents of the book. The problem revolves around an uncertain linear system x(O) = x~ in R", where 0 E {1, ... , N} is a random variable representing this uncertainty and (Ai' B , C) and xJ are the coefficient matrices and initial state, respectively, of j j a linear control system, for eachj = 1, ... , N. A common assumption is that the mechanism causing this uncertainty is additive noise, and that conse­ quently the "controller" has access only to the observation process y( . ) where y = Cex +~.

Keywords

Random variable control control system stabilization system

Authors and affiliations

  1. 1.Mathematics DepartmentTemple UniversityPhiladelphiaUSA

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