Flexible Prescribed-Time Optimal Control With Adaptive State–Input Constraint Bounds via Actor–Critic Learning

This article develops a prescribed-time (PT) optimal tracking framework for nonlinear systems with concurrent state and input constraints. The main focus is a flexible PT constraint-handling mechanism that is introduced first in the design: a time-varying auxiliary function performs PT error transformation, while a state-triggered adaptation law adjusts state/input performance envelopes online. Specifically, the envelopes are relaxed only when constraint violation risk is detected and are otherwise kept tight, which reduces the conservatism of fixed-boundary designs, enlarges feasible operation regions, and preserves safety margins. Based on the resulting unconstrained error dynamics, to achieve optimality within this framework, an actor-critic adaptive dynamic programming (ADP) scheme is constructed to solve the nonautonomous Hamilton-Jacobi-Bellman (HJB) equation online, guaranteeing user-assigned convergence accuracy and time independently of initial conditions. Rigorous analysis proves uniform ultimate boundedness of all closed-loop signals and PT convergence of the tracking error. Simulations on a general nonlinear system and a fault-tolerance tracking scenario, with comparisons to representative baselines under different initial conditions, verify the proposed method's superior transient tracking and reliable convergence-time performance.