Cooperative Output Regulation Under Transmission Delays: A Direct Data-Driven Hybrid Event-Triggered Approach

Abstract

This paper addresses the event-triggered cooperative output regulation problem for heterogeneous multi-agent systems with unknown system model and transmission delays. First, hybrid event-triggering mechanism (ETM) and distributed observer are developed to estimate exosystem’s state, with the hybrid ETM, designable minimum event-triggering interval can be achieved, i.e., strong Zeno-freeness. Second, a hybrid model consisting of flow dynamics and jump dynamics is constructed to describe closed-loop dynamics, which incorporates the hybrid ETM, transmission delays and auxiliary variables. Third, data collection is performed via the proposed filters such that precise real-time derivative measurement is avoided, and matrix equation is constructed to solve the regulator equations with explicit solvability conditions, and control gains are solved by data-based matrix inequalities with extra free decision matrix. Then, a Lyapunov function with respect to tracking errors, auxiliary functions, measurement errors and internal variables is constructed, which is useful for stability analysis and design and also has its own significance. Finally, simulation and experimental results are provided to verify the obtained results. Note to Practitioners—This paper addresses a practical problem in coordinating multiple dynamic systems (such as distributed generators, robots, or autonomous vehicles) when their communication networks introduce transmission delays and their internal dynamic models are completely unknown. Unlike most existing methods that rely on accurate mathematical models of each agent, which are often unavailable or expensive to obtain in practice, this paper proposes a data-driven hybrid event-triggered control approach that uses only measured data, without requiring any system identification. The proposed data-driven method automatically learns the necessary control gains and inherently compensates for transmission delays, eliminating the need for delay modeling or complex delay compensation schemes. The event-triggering mechanism reduces communication among agents and saves network communication resources. Importantly, it guarantees a minimum time between consecutive triggers (strong Zeno-freeness), preventing the controller from reacting infinitely fast, which is a critical feature for digital implementation. By integrating data-driven techniques with delay-tolerant event-triggered control, the proposed approach offers a practical and implementable solution for networked multi-agent systems with communication delays and unknown dynamics.