Unified ETM-based Consensus Control for Nonlinear MASs: An Improved Dual-Level Game Approach with Event-Triggered Neural Networks

This paper addresses the event-triggered consensus control problem for nonlinear multi-agent systems (MASs) under resource constraints, where a unified event-triggered mechanism (ETM) is proposed to conserve system resources through discrete updates of both control laws and neural networks (NNs). First, an improved dual-level game approach is developed specifically for ETM design, treating the control law and event-triggered error as adversarial players to derive an optimal control law and a maximum allowable trigger error threshold. Unlike existing dual-level game-based ETMs, whose parameter design relies on an unknowable constant bounding the cost function gradient norm with respect to the consensus error, the proposed improved approach eliminates this dependency. Second, within the adaptive dynamic programming (ADP) framework, event-triggered NNs reduce computational load by updating weights solely at triggering instants with rigorous theoretical guarantees establishing the quantitative relationship between weight estimation errors and cost functions. Third, the unified ETM coordinates control execution and NN updates via logical “union” relations, ruling out both Zeno and singular phenomena. Simulations validate its effectiveness and superiority.