A game theoretic approach to distributed control of homogeneous multi-agent systems

Abstract

A distributed multi-agent system consisting of homogeneous agents is considered in this paper. Distributed differential games and their solutions in terms of Nash equilibria are defined for such systems, both in a linear quadratic setting and in a general, nonlinear setting. As with standard differential games, obtaining exact solutions for nonlinear distributed differential games requires solving coupled partial differential equations, closed-form solutions for which are not readily available in general. A systematic method for constructing approximate solutions for a nonlinear distributed differential game with two players is provided. The method requires solving algebraic equations only and is illustrated on a numerical example.