Online [formula omitted] control for continuous-time nonlinear large-scale systems via single echo state network

Abstract

In this article, the H∞ optimal control for nonlinear large-scale interconnected systems is designed using novel adaptive/approximate dynamic programming (ADP) method and single echo state network (ESN). All subsystems of the large-scale systems are combined into an augmented system. Subsequently, the H∞ problem is transformed into a zero-sum game problem, where a nonlinear partial differential Hamilton-Jacobi-Isaacs (HJI) equation is required to be solved. However, the HJI equation has no analytically solution, so this paper develops a novel online ADP algorithm to approximatively obtain the index function and control policy simultaneously employing single ESN without requiring the initial admissible control. The stability of the closed-loop augmented system and the ESN output weights is analyzed using the Lyapunov theorem and guaranteed to be uniformly ultimate boundedness (UUB). A large-scale system example including three subsystems is simulated to show the feasibility of the suggested control scheme.