A Nash Game Approach to Mixed H2/H∞ Control

D. J.N. Limebeer; B. Hendel; B. D.O. Anderson

doi:10.1109/9.273340

A Nash Game Approach to Mixed H₂/H_∞ Control

D. J.N. Limebeer, B. Hendel, B. D.O. Anderson

School of Engineering

Research output: Contribution to journal › Article › peer-review

282 Citations (Scopus)

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.

Original language	English
Pages (from-to)	69-82
Number of pages	14
Journal	IEEE Transactions on Automatic Control
Volume	39
Issue number	1
DOIs	https://doi.org/10.1109/9.273340
Publication status	Published - Jan 1994

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A Nash Game Approach to Mixed H₂/H_∞ Control

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