Adaptive tracking control for stochastic nonlinear state-constrained systems with input delay based on multi-dimensional Taylor network

Abstract

In this paper, an adaptive tracking control strategy based on multi-dimensional Taylor network (MTN) is proposed for a class of stochastic nonlinear state-constrained systems with input delay. Firstly, to avoid constraint violation, the adaptive backstepping approach and barrier Lyapunov function (BLF) are combined in a unified framework. Then, a suitable auxiliary system with the same order as the considered system is constructed to deal with the effect of input delay. In addition, MTN is used to estimate unknown nonlinear functions during the design of the controller. Furthermore, with the help of the Lyapunov stability theorem, the controller presented in this paper can guarantee that all the closed-loop signals are bounded in probability, the system states remain in the defined compact sets, the output signal can track the reference signal successfully, and the tracking error is bounded by the expected bound. Finally, two examples are given to verify the effectiveness of the designed scheme.

Keywords:

• Adaptive control
• multi-dimensional Taylor network (MTN)
• stochastic nonlinear input delay system
• full-state constraints
• barrier Lyapunov function
• auxiliary system

Disclosure statement

No potential conflict of interest was reported by the author(s).