Zero-Sum Game-Based Decentralized Optimal Control for Saturated Nonlinear Interconnected Systems via a Data and Event Driven Approach
Shihui Liu, Ben Niu, Ning Xu, Xudong Zhao
Abstract
This article proposes a decentralized optimal zero-sum game method for nonlinear interconnected systems with asymmetric input constraints and external disturbances based on a data- and event-driven approach. First, by assigning a particular cost function for each isolated subsystem with disturbances, the decentralized control problem is equivalently converted into finding a sequence of optimal zero-sum game schemes. Then, a recurrent neural network-based data-driven model is designed to reconstruct the system, ensuring that the acquired results are applicable in a broad range of contexts. After obtaining the system model, an event-triggered adaptive dynamic programming algorithm is used to approximate the Nash equilibrium solutions of Hamilton–Jacobi–Isaacs equations under a critic architecture. A noteworthy characteristic is that the critic updating laws are designed via an experience replay technology, such that the persistence of excitation condition can be excluded. Finally, all signals of the close-loop system are guaranteed to be uniformly ultimately bounded based on the Lyapunov stability theory, and a simulation example is presented to exemplify the effectiveness of the proposed decentralized optimal zero-sum game scheme.