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

Abstract

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.

A Game Theoretic Framework for Distributed Control of Multi-Agent Systems with Acyclic Communication Topologies

“…Corollary 1: Suppose Assumption 1 holds and consider the linear autonomous system described by the dynamicsẊ i = (A i (0) + A Ni (0, 0)) X i . Suppose there exists a symmetric positive definite matrixP i ∈ R (ni+ni)×(ni+ni) such that (18) for i = 1, . .…”

Distributed Control of Multi-Agent Systems via Linear Quadratic Differential Games with Partial Information

“…In what follows we build on preliminary works in [17], [18]. Considering MAS with limited communication, we define linear quadratic differential games with partial information and exploit the resulting framework to design distributed control laws for each agent in the MAS.…”

“…. , 4, corresponding to the closed-loop system (24)-(18). Initial and final positions are denoted by the crosses and solid diamond markers, respectively.…”