A Cyclic-Small-Gain-Based Adaptive Fuzzy Control of Interconnected Systems

This article investigates a novel adaptive fuzzy decentralized output-feedback control method for a class of uncertain large-scale interconnected nonlinear systems with unknown dynamics and immeasurable states. By employing fuzzy logic systems, the unknown nonlinear dynamics are estimated. Moreover, the immeasurable states are approximated by constructing a fuzzy decentralized state observer. Based on the Lyapunov stability theory and decentralized backstepping technique, the Lyapunov functions are constructed in a recursive way for each subsystem. In the last step of our process, an overall Lyapunov function is proposed to realize the control objective. Differing from other works, the interconnection influence of the large-scale system is compensated with a more relaxed assumption by introducing the cyclic-small-gain condition. Under the proposed control method, the closed-loop system is capable of being semiglobally uniformly ultimately bounded. Furthermore, the observer and stabilizing errors are able to be bounded by an arbitrarily small residual set around the origin. Finally, a simulation with comparison is provided to illustrate the viability of the presented control scheme.