Adaptive Tracking Control for Stochastic Nonlinear Time-Delay Systems With Full-State Constraints and Input Saturation Based on Multi-Dimensional Taylor Network

For stochastic nonlinear time-delay systems with full-state constraints and input saturation, the existing control methods cannot be directly applied. To solve the control problem, an adaptive tracking control scheme is proposed here. The barrier Lyapunov function (BLF) and Lyapunov-Krasovskii functional (LKF) are combined in a unified framework. The former is to prevent the violation of state constraints and the latter is to address the impact of time delay. A suitable auxiliary system with the same order as the considered system is constructed to compensate for input saturation. Moreover, the multi-dimensional Taylor network (MTN) is introduced to estimate unknown nonlinear functions in the process of controller design. With the help of the Lyapunov stability theorem and the backstepping technique, an adaptive MTN tracking controller is developed to ensure that all the closed-loop signals remain bounded in probability and that the system state constraints are never violated while the output signal tracks the reference one successfully. Simulation examples with three types of reference signals (y(d) = 0.5 sin (2t), y(d) = 0.9 and the square reference signal) are provided to verify the validity of the designed control approach.