Title :
A Nash game approach to mixed H2/H∞ control
Author :
Limebeer, D.J.N. ; Anderson, B.D.O. ; Hendel, B.
Author_Institution :
Dept. of Electr. Eng., Imperial Coll. of Sci., Technol. & Med., London, UK
fDate :
1/1/1994 12:00:00 AM
Abstract :
The established theory of nonzero sum games is used to solve a mixed H2/H∞, control problem. Our idea is to use the two pay-off functions associated with a two-player Nash game to represent the H2 and H∞ criteria separately. We treat the state-feedback problem and we find necessary and sufficient conditions for the existence of a solution. Both the finite and infinite time problems are considered. In the infinite horizon case we present a full stability analysis. The resulting controller is a constant state-feedback law, characterized by the solution to a pair of cross-coupled Riccati equations, which may be solved using a standard numerical integration procedure. We begin our development by considering strategy sets containing linear controllers only. At the end of the paper we broaden the strategy sets to include a class of nonlinear controls. It turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers
Keywords :
feedback; game theory; linear systems; nonlinear control systems; optimal control; Nash game approach; constant state-feedback law; cross-coupled Riccati equations; finite time; infinite horizon; infinite time; linear controllers; mixed H2/H∞ control; necessary and sufficient conditions; nonlinear controls; nonzero sum games; numerical integration; pay-off functions; stability analysis; state-feedback; strategy sets; Cost function; Entropy; Game theory; Hydrogen; Infinite horizon; Riccati equations; Stability analysis; State feedback; Sufficient conditions; Upper bound;
Journal_Title :
Automatic Control, IEEE Transactions on
