Adaptive neural dynamic surface control for full state constrained stochastic nonlinear systems with unmodeled dynamics

Abstract This paper solves the problem of adaptive neural dynamic surface control (DSC) for a class of full state constrained stochastic nonlinear systems with unmodeled dynamics. The concept of the state constraints in probability is first proposed and applied to the stability analysis of the system. The full state constrained stochastic nonlinear system is transformed to the system without state constraints through a nonlinear mapping. The unmodeled dynamics is dealt with by introducing a dynamic signal and the adaptive neural dynamic surface control method is explored for the transformed system. It is proved that all signals of the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded(SGUUB) in mean square or the sense of four-moment. At the same time, the full state constraints are not violated in probability. The validity of the proposed control scheme is demonstrated through the simulation examples.

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