Adaptive prescribed-time control for state-constrained non-linear systems with input delay

Abstract In this article, the adaptive prescribed-time control is studied for a class of non-linear systems. Different from the existing results, an adaptive prescribed-time tracking controller is constructed to eliminate the uncertainties arising from state constraints, input delay and parametric non-linearities. Firstly, the parametric non-linearities of the system are addressed by adaptive control and parameter separation technique. By integrating the Pade approximation method with the barrier Lyapunov function in a unified framework, the uncertainties caused by input delay and state constraints are effectively tackled. Then, an adaptive prescribed-time state-feedback control strategy is proposed based on the backstepping design procedure and rigorous stability analysis, which can make the tracking error of the system converge to the origin in the prescribed time, all the signals in the closed-loop system are uniformly ultimately bounded, and the system state constraints are never violated. Finally, a simulation example is provided to show the effectiveness of the proposed control strategy.