Adaptive Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints and Unknown Covariance Noise

Abstract This paper is devoted to the adaptive state-feedback tracking control for stochastic nonlinear systems disturbed by unknown covariance noise under the condition of full-state constraints and parametric uncertainties. Different from the related literatures, nonlinear functions in the diffusion terms are allowed to be unknown in this paper. The parametric uncertainties and unknown covariance noise are compensated with the aid of adaptive control design. By combining the backstepping technique with barrier Lyapunov function (BLF) in a unified framework, the full-state constraints can be dealt. Then, an adaptive state-feedback controller is constructed, which guarantees all the signals in the closed-loop system are uniformly ultimately bounded, the system states remain in the defined compact sets and the output tracks the reference signal well. Finally, stochastic noise is introduced to establish a stochastic simple pendulum system to show the effectiveness of the proposed controller.

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