Game-Based Distributed Control for Multiple Euler–Lagrange Systems over Switching Topologies

Abstract

This article investigates the controller design for a game-based distributed control problem for multiple Euler–Lagrange systems over switching topologies, in which the objective is to stabilize each Euler–Lagrange system and minimize the local cost function of an agent simultaneously. The communication topologies are switching among a set of weight-balanced digraphs, and the dynamic of an Euler–Lagrange agent includes unknown parts. In this problem, agents have limited observation of others' states, but agents can estimate other states by exchanging information with their neighbors over switching topologies. The coupling states of agents, uncomplete states, and switching topologies are such that existing distributed control strategies cannot address this problem. In this regard, two distributed controllers are respectively proposed for this game-based distributed control problem with known and unknown dynamics based on the feedback linearization, consensus-based estimation, gradient play, and integral compensation. Based on the time-scale decomposition technique and orthogonal decomposition method, it proves that the proposed controllers can stabilize the Euler–Lagrange agent and are such that the local state is pushed to the Nash equilibrium, and the communication topology is allowed to be arbitrarily switched among different digraphs. Lastly, the simulation demonstrates the effectiveness of proposed controllers.