Robust H-infinity Output Feedback Control for Nonlinear Systems

Abstract

The study of robust nonlinear control has attracted increasing interest over the last few years. Progress has been aided by the recent extension of the linear quadratic results which links the theories of L2 gain control (nonlinear H∞ control), differential games, and stochastic risk sensitive control. In fact, significant advances in both linear and nonlinear H∞ theory have drawn upon results from the theories of differential games and stochastic risk sensitive control. Despite these advances in H∞ control theory, practical controllers for complex nonlinear systems which operate on basic H∞ principles have not been realized to date. Issues of importance to the design of a practical controller include (i) computational complexity, (ii) operation solely with observable quantities, and (iii) implementability in finite time. In this dissertation we offer a design procedure which yields, practical and implementable H∞ controllers and meets the, mandate of the above issues for general nonlinear systems. In particular, we develop a well defined and realistically implementable procedure for designing robust output feedback controllers for a large class of nonlinear systems. We analyze this problem in both continuous time and discrete time settings. The robust output feedback control problem is formulated as a dynamic game problem. The solution to the game is obtained by transforming the problem into an equivalent full state feedback problem where the new state is called the information state. The information state method provides a separated control policy which involves the solution of a forward and a backward dynamic programming equation. Obtained from the forward equation is the information state, and from the backward equation is the value function of the game and the optimal information state control. The computer implementation of the information state controller is addressed and several approximations are introduced. The approximations are designed to decrease the online computational complexity of controller.