Finite Horizon H∞ and Related Control Problems

Book excerpt: HIS book presents a generalized state-space theory for the analysis T and synthesis of finite horizon suboptimal Hoo controllers. We de rive expressions for a suboptimal controller in a general setting and propose an approximate solution to the Hoo performance robustness problem. The material in the book is taken from a collection of research papers written by the author. The book is organized as follows. Chapter 1 treats nonlinear optimal control problems in which the cost functional is of the form of a quotient or a product of powers of definite integrals. The problems considered in Chap ter 1 are very general, and the results are useful for the computation of the actual performance of an Hoo suboptimal controller. Such an application is given in Chapters 4 and 5. Chapter 2 gives a criterion for the evaluation of the infimal Hoc norm in the finite horizon case. Also, a differential equation is derived for the achievable performance as the final time is varied. A general suboptimal control problem is then posed, and an expression for a subopti mal Hoo state feedback controller is derived. Chapter 3 develops expressions for a suboptimal Hoo output feedback controller in a very general case via the solution of two dynamic Riccati equations. Assuming the adequacy of linear expressions, Chapter 4 gives an iterative procedure for the synthesis of a suboptimal Hoo controller that yields the required performance even under parameter variations.