Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

Abstract

In this paper, a novel decentralized adaptive neural control approach based on the backstepping technique is proposed to design a decentralized H∞ adaptive neural controller for a class of stochastic large-scale nonlinear systems with external disturbances and unknown nonlinear functions. RBF neural networks are utilized to approximate the packaged unknown nonlinearities. A novel concept with regard to bounded-H∞ performance is proposed. It can be applied to solve an H∞ control problem for a class of stochastic nonlinear systems. The constant terms appeared in stability analysis are dealt with by using Gronwall inequality, so that H∞ performance criterion is satisfied. The assumption that the approximation errors of neural networks must be square-integrable in some literature can be eliminated. The design process for decentralized bounded-H∞ controllers is given. The proposed control scheme guarantees that all the signals in the resulting closed-loop large-scale system are uniformly ultimately bounded in probability, and each subsystem possesses disturbance attenuation performance for external disturbances. Finally, the simulation results are provided to illustrate the effectiveness and feasibility of the proposed approach.