BLF-based adaptive DSC for a class of stochastic nonlinear systems of full state constraints with time delay and hysteresis input

Abstract

This paper is concerned about barrier Lyapunov function(BLF)-based adaptive dynamic surface control(DSC) for a class of stochastic nonlinear systems of full state constraints with hysteresis input and time delay. All states of the system are guaranteed to be constrained in bounded compact set. The pure feedback nonlinear system is transformed into a strictly feedback nonlinear system with nonaffine nonlinear terms by using the mean value theorem. By using backstepping design of BLF combine with DSC technique, the explosion of complexity is avoided. Based on the neural network with the finite covering lemma, the time-delay functions are solved. Simultaneously, the backlash-like hysteresis input control in this paper is considered. The two cases of symmetric and asymmetric BLFs are discussed separately. An adaptive controller is designed to ensure that the output tracking error converges on a small region of the origin. Finally, the control scheme ensures that all signals in the closed-loop systems are semi-global uniformly ultimately bounded. Results of two simulation cases are presented to prove the effectivity of the theoretical analysis.