Pareto-Nash Equilibrium in Multiobjective Formation Control Problems

Abstract

The formation control of teams of agents constitutes an important class of multiagent control systems. We combine control, graph and game theories to address a particular formation control problem – the formation tracking problem – in the context of the multiobjective noncooperative game theory. The solution concept proposed for the problem is the Pareto-Nash equilibrium, which is at the same time a Nash equilibrium (stable, self-enforcing) and, with respect to the Nash equilibrium, Pareto-optimal for each agent in the formation. A numerical example illustrates the main characteristics and contributions brought by the approach and solution concept proposed.