Distributed strategy-updating rules for aggregative games of multi-integrator systems with coupled constraints

TL;DR

This paper introduces a distributed strategy-updating rule for multi-integrator agents in aggregative games with coupled constraints, enabling convergence to Nash equilibrium using limited local information and neighbor communication.

Contribution

It proposes a novel distributed strategy-updating rule combining Lagrange multiplier coordination and aggregator estimation for multi-integrator agents.

Findings

The proposed rule guarantees convergence to Nash equilibrium.

Effectiveness demonstrated through Lyapunov and singular perturbation analysis.

Numerical examples validate theoretical results.

Abstract

In this paper, we explore aggregative games over networks of multi-integrator agents with coupled constraints. To reach the general Nash equilibrium of an aggregative game, a distributed strategy-updating rule is proposed by a combination of the coordination of Lagrange multipliers and the estimation of the aggregator. Each player has only access to partial-decision information and communicates with his neighbors in a weight-balanced digraph which characterizes players' preferences as to the values of information received from neighbors. We first consider networks of double-integrator agents and then focus on multi-integrator agents. The effectiveness of the proposed strategy-updating rules is demonstrated by analyzing the convergence of corresponding dynamical systems via the Lyapunov stability theory, singular perturbation theory and passive theory. Numerical examples are given to illustrate our results.