Adaptive Multi-Dimensional Taylor Network Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints and Input Saturation

In this study, an adaptive tracking controller using multi-dimensional Taylor network (MTN) is presented for state-constrained nonlinear stochastic systems with saturated input, in which MTN is implemented to model the unknown nonlinear functions. Firstly, the barrier Lyapunov function (BLF) and backstepping technique are combined under a unified framework to eliminate the impact of full-state constraints. Then, the effect raised by saturated input is solved by introducing an appropriate auxiliary system. Furthermore, by employing the Lyapunov stability theorem, the designed adaptive controller could ensure that all closed-loop signals are bounded in probability, the output signal can track the desired signal successfully, the tracking error is bounded by the expected bound, and the system state constraints are never violated. Finally, the efficiency of the suggested control methodology is confirmed by providing an example.