Backstepping-based decentralized adaptive neural $$H_{\infty }$$ H ∞ control for a class of large-scale nonlinear systems with expanding construction

Abstract

In this paper, a backstepping-based robust decentralized adaptive neural \( H_{\infty }\) connective stabilization approach is proposed for a class of large-scale interconnected nonlinear systems with expanding construction and external disturbances. First, the decentralized adaptive neural \(H_{\infty }\) controllers for the original nonlinear interconnected system are deduced and obtained by using backstepping technique, which can guarantee the connective stability of the nonlinear interconnected system. Then, the expansion of the system is considered. It is needed that the decentralized control laws and adaptive laws of the original system are kept to be unchanged, and only the control and adaptive laws for the new subsystem needs to be designed. Based on this requirement, a backstepping-based decentralized adaptive neural \(H_{\infty }\) control design method for the new subsystem is given. The decentralized control law and adaptive law of the new subsystem can stabilize the resultant expanded large-scale nonlinear system. The proposed method can guarantee the connective stability of the expanded large-scale nonlinear system. In this paper, neural networks are used to approximate the packaged nonlinear terms. As a result, the calculation of the control laws and adaptive laws is simplified. The effect of external disturbances and approximation errors is attenuated by \( H_{\infty }\) performance. All of the signals in the expanded closed-loop system are bounded. Two numerical examples are provided to show the effectiveness of the proposed control approach.