Reduced-order K-filters based decentralized fuzzy adaptive control of stochastic large-scale nonlinear systems with stochastic input unmodeled dynamics

This paper addresses a decentralized fuzzy adaptive control scheme for stochastic large-scale systems in the presence of stochastic input unmodeled dynamics, which is a novel problem on the research of unmodeled dynamics. The stochastic nonlinear input unmodeled dynamics is restricted to be stochastic input-to-state stable. We introduce changing supply function to deal with the stochastic input unmodeled dynamics and construct the corresponding small gain condition. Due to partial states unavailable for measurement and control gains unknown, we design reduced-order K-filters to estimate the unmeasurable states only. First type fuzzy systems are adopted to approximate the whole of the black-box functions and the unknown continuous system functions, which can degrade the complexity of calculation and simply the K-filters' structure. Utilizing the changing supply function, dynamic surface control (DSC) method and Chebyshev's inequality, a strict stability analysis in probability is made. The analysis shows that the control laws can guarantee all the signals to be semi-globally uniformly ultimately bounded (SGUUB) in mean square or the sense of four-moment. Simulation results illustrate the effectiveness of the approach.