Necessary and Sufficient Conditions for Nonlinear Worst Case (H-Infinity) Control and Estimation

Arthur J. Krener, University of California, Davis

The standard H-Infinity control problem is to design a compensator which processes the measured output of a plant and returns a contolled input so as to minimize the worst case effect of the unmeasured, uncontrolled input on the the regulated output. Originally the problem was posed for linear time invariant systems in the frequency domain and solved using H-Infinity methods. Doyle, Glover and others rephrased the problem in a state space discription and reduced it to the solution of a pair of algebraic Riccati equations. The state space approach has been partially generalized to nonlinear, time varying systems by several authors. We shall present the complete nonlinear generalization by giving necessary and sufficient conditions for the existence of a compensator with worst case gain less than a specified constant.We show how the nonlinear problem can be reduced to the solution of a pair partial differential equations of Hamilton-Jacobi type. These are the generalization of the Riccati equations in the linear setting.