Decentralized Event-Triggered Control for a Class of Nonlinear-Interconnected Systems Using Reinforcement Learning

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In this article, we propose a novel decentralized event-triggered control (ETC) scheme for a class of continuous-time nonlinear systems with matched interconnections. The present interconnected systems differ from most of the existing interconnected plants in that their equilibrium points are no longer assumed to be zero. Initially, we establish a theorem to indicate that the decentralized ETC law for the overall system can be represented by an array of optimal ETC laws for nominal subsystems. Then, to obtain these optimal ETC laws, we develop a reinforcement learning (RL)-based method to solve the Hamilton-Jacobi-Bellman equations arising in the discounted-cost optimal ETC problems of the nominal subsystems. Meanwhile, we only use critic networks to implement the RL-based approach and tune the critic network weight vectors by using the gradient descent method and the concurrent learning technique together. With the proposed weight vectors tuning rule, we are able to not only relax the persistence of the excitation condition but also ensure the critic network weight vectors to be uniformly ultimately bounded. Moreover, by utilizing the Lyapunov method, we prove that the obtained decentralized ETC law can force the entire system to be stable in the sense of uniform ultimate boundedness. Finally, we validate the proposed decentralized ETC strategy through simulations of the nonlinear-interconnected systems derived from two inverted pendulums connected via a spring.

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IEEE Transactions on Cybernetics