Finite horizon \(H\infty\) and related control problems
The book is devoted to state-space theory for the analysis and synthesis of finite horizon suboptimal \(H_ \infty\) controllers. It contains six chapters. The first one treats nonlinear optimal control problem in which the ``nonstandard'' cost functional has the form of a quotient or a product of powers of definite integrals. The authors use Dubovitskii-Milyutin techniques to derive necessary conditions for optimality. In the second chapter, an open loop solution to a finite horizon \(H_ \infty\) optimal control problem is presented. A general suboptimal control problem is then posed and an expression for a feedback controller is derived by solving a dynamic Riccati equation. The chapter also presents techniques for the computation of the optimal and suboptimal performance. Chapter 3 develops expressions for a suboptimal \(H_ \infty\) output feedback controller in the general case via the solution of two dynamic Riccati equations. In chapter 4, the authors consider the finite horizon \(H_ \infty\) performance robustness problem with parameter variations. An iterative procedure for the synthesis of a suboptimal \(H_ \infty\) controller and an expression for the variation of performance due to parameter variations are given in this case. Chapter 5 treats a general minimization problem in which the cost functional is a quotient of definite integrals. The results are shown to have application to the finite horizon \(H_ \infty\) performance robustness problem. An expression for the variation of performance in terms of variations in the system matrices is developed. The last chapter is devote to the applications of finite horizon \(H_ \infty\) techniques to problems of design for an automatic landing system. The book is well composed, contains many examples and bibliographical references and can be recommended to everyone interested in the subject.
scientific article; zbMATH DE number 750182