Minimum Entropy H_ Control (Lecture Notes in Control and Information Sciences, 146)

This monograph is concerned with the design of feedback controllers for linear multivariable systems, which are robust to system uncertainty. System uncertainty can be realistically represented by including perturbations with bounded H?-norm, and this is the approach taken here. For a given H?-norm bound, there is a family of robustly stabilizing controllers, and the central question in this book is which of these controllers to choose. One choice to take is that which minimizes the enthropy of the resulting closed loop transfer function, and the derivation and properties of this solution occupies most of this monograph. Explicit formulae are obtained for the minimum enthropy solution, which is a precisely defined compromise between the Linear Quadratic Gaussian optimal solution and the H?-optimal solution. The book will be appropriate for graduate classes requiring only a first course in state-space methods, and some elementary knowledge of H? control and Linear Quadratic Gaussian control. Introduction....Pages 1-5 The entropy of a system....Pages 7-14 The minimum entropy $$\mathcal{H}_\infty$$ control problem....Pages 15-33 The minimum entropy $$\mathcal{H}_\infty$$ distance problem....Pages 35-47 Relations to combined $$\mathcal{H}_\infty$$ /LQG control....Pages 49-58 Relations to risk-sensitive LQG control....Pages 59-63 The normalized $$\mathcal{H}_\infty$$ control problem....Pages 65-77 $$\mathcal{H}_\infty$$ -characteristic values....Pages 79-101 LQG and $$\mathcal{H}_\infty$$ monotonicity....Pages 103-109 D. Mustafa, K. Glover. On T.p. [infinity] Appears As The Infinity Symbol, Subscript. Includes Bibliographical References And Index.