Adaptive Neural Tracking of Uncertain State-Constrained Nonlinear Systems With Unmatched Disturbances: Prescribed-Time Disturbance Observer Approach

We propose a prescribed-time nonlinear disturbance observer (PTNDO) approach for adaptive prescribed-time tracking of state-constrained strict-feedback systems with unmatched disturbances and nonlinearities. In contrast to existing control methods that address the state constraint problem, the key contribution of this article is the development of a neural-network-based adaptive PTNDO to compensate for unmatched disturbances within a prescribed time while dealing with unknown nonlinearities in the field of the adaptive prescribed-time tracking. Based on a nonlinear transformation function technique that eliminates the conventional feasibility conditions of virtual control laws in recursive design steps, the original state-constrained system is transformed into an unconstrained system. Subsequently, by deriving a practical prescribed-time adjustment function and its related stability lemma, a PTNDO-based adaptive control strategy is established to guarantee that the disturbance observation and tracking errors converge to the adjustable bound, including zero at a prescribed settling time, while maintaining state constraints. Simulation results verify the resulting approach.