Worst Case Learning for H ∞ Consensus for Heterogeneous Multiagent Systems: A Resource-Constrained Game Approach.

Abstract

This article investigates heterogeneous high-order nonlinear multiagent systems (MASs) under an event-triggered mechanism (ETM). A reinforcement learning (RL)-based zero-sum game (ZSG) approach is employed to solve the robust consensus problem. To handle heterogeneity, unified-dimension state variables are constructed, auxiliary variables are defined, and consensus errors are reformulated accordingly. By applying the min-max principle, the optimal $H_{\infty } $ consensus problem is transformed into a ZSG problem, and an approximately optimal consensus protocol is derived by solving the Hamilton-Jacobi-Isaacs (HJI) equation with the proposed actor-critic-identifier (ACI) learning framework. In particular, a novel ACI network is developed to approximate the HJI solution, while a hybrid distributed ETM with adaptive dynamic thresholds is designed to avoid redundant communication and computation. An error-oriented Lyapunov method is used to establish convergence bounds for the consensus error and to exclude the Zeno behavior. Numerical simulations validate the effectiveness of the proposed algorithm.