Control Design for Stochastic Nonlinear Systems with Full-state Constraints and Input Delay: A New Adaptive Approximation Method

In this paper, the full state constraints and input delay of stochastic nonlinear systems are studied. A new adaptive control algorithm is proposed using backstepping approach and multi-dimensional Taylor network (MTN) method. Firstly, the input delay problem is dealt with by introducing a new variable using the Padé approximation with Laplace transform. Secondly, MTNs are employed to approximate unknown nonlinear functions, and the barrier Lyapunov functions (BLFs) are constructed to deal with the state constraints. Based on this, a new approximation-based adaptive controller is proposed. Thirdly, it is proved that the proposed control method can ensure that all signals in the closed-loop system are semi-global ultimately uniformly bounded (SGUUB) in probability and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to illustrate the effectiveness of the proposed design method.