Adaptive decentralized control for a class of interconnected nonlinear systems via backstepping approach and graph theory

This paper is concerned with the adaptive decentralized control problem for a class of interconnected nonlinear systems, where the interconnections are assumed to be unknown and completely nonlinear. In addition, the interconnections and their bounds are allowed to contain the states of all subsystems. The main contribution is that, a strictly decentralized control scheme with compensation mechanism is developed to achieve the desirable tracking performance. More specifically, a smooth switching function is introduced to construct adaptive control laws, where the compensation mechanism is activated only if the immediate variable involved in the backstepping design exceeds a given constant, otherwise it will be turned-off. Furthermore, by combining graph theory and Lyapunov analysis method, it is proved that all the signals of the resulting closed-loop system are globally bounded, and the tracking errors of subsystems exponentially converge to a compact set, whose radius is adjustable by choosing different controller design parameters. Finally, the effectiveness of the proposed adaptive decentralized control scheme is illustrated with a simulated example.