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A class of uncertain nonlinear systems that are additionally driven by unknown covariance noise is considered. Based on the backstepping technique, adaptive neural control schemes are developed to solve the output tracking control problem of such systems. As it is proven by stability analysis, the proposed controller guarantees that all the error variables are bounded with desired probability in a compact set while the tracking error is mean-square semiglobally uniformly ultimately bounded (M-SGUUB). The tracking performance and the effectiveness of the proposed design are evaluated by simulation results.