Dynamic Event-Triggered Control for Human–Machine Cooperative Systems Based on Dynamic Authority Allocation

This article addresses the challenging problem of constrained optimal control for human–machine systems subject to external disturbances and the bounded rationality of the human operator. To this end, a novel game-theoretic framework is proposed. Unlike monolithic game formulations, the framework uniquely disaggregates the control problem by transforming it into a multifaceted game via logarithmic barrier functions (BFs): it models human–machine cooperation as a positive-sum game oriented toward shared objectives, and disturbance rejection as a zero-sum game tailored for robustness enhancement. To capture the nonideal human decision-making, we integrate the level-$k$reasoning framework to model the operator’s bounded cognitive dynamics. The corresponding coupled Hamilton–Jacobi–Isaacs (HJI) equations for this human–machine game are derived, and critically, a rigorous proof of global asymptotic stability (GAS) for the transformed system is provided, establishing a solid theoretical foundation. For online implementation without requiring prior knowledge of the system dynamics, we develop a resource-efficient learning architecture based on the adaptive dynamic programming (ADP) and a novel dynamic event-triggered mechanism (DETM). A key feature of this architecture is a fuzzy logic-based module for dynamic authority allocation, which adaptively adjusts control sharing in real time. Rigorous analysis demonstrates that all signals in the closed-loop system are uniformly ultimately bounded and that Zeno behavior is precluded. Simulation results are presented to validate the effectiveness and superiority of the proposed control strategy.