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 |
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Pages (from-to) | 69-82 |
Number of pages | 14 |
Journal | IEEE Transactions on Automatic Control |
Volume | 39 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 1994 |
Externally published | Yes |
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering