A Nash Game Approach to Mixed H2/H Control

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

Research output: Contribution to journalArticlepeer-review

279 Citations (Scopus)


The established theory of nonzero sum games is used to solve a mixed H2/Hcontrol 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 languageEnglish
Pages (from-to)69-82
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - Jan 1994
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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