Adaptive fuzzy decentralized control for large-scale nonlinear systems with time-varying delays and unknown high-frequency gain sign.

In this paper, an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large-scale strict-feedback nonlinear systems without the measurements of the states. The nonlinear systems in this paper are assumed to possess unstructured uncertainties, time-varying delays, and unknown high-frequency gain sign. Fuzzy logic systems are used to approximate the unstructured uncertainties, K-filters are designed to estimate the unmeasured states, and a special Nussbaum gain function is introduced to solve the problem of unknown high-frequency gain sign. Combining the backstepping technique with adaptive fuzzy control theory, an adaptive fuzzy decentralized robust output feedback control scheme is developed. In order to obtain the stability of the closed-loop system, a new lemma is given and proved. Based on this lemma and Lyapunov-Krasovskii functions, it is proved that all the signals in the closed-loop system are uniformly ultimately bounded and that the tracking errors can converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated from simulation results.