Prescribed‐Time Safe Actor–Critic Reinforcement Learning for Nonlinear Markov Jump Systems With Barrier‐Function Obstacle Avoidance

ABSTRACT

This study studies generator‐assisted prescribed‐time safe actor–critic reinforcement learning for continuous‐time nonlinear Markov jump systems with boundary and obstacle constraints. A mode‐dependent critic approximates a Markov‐generator value function, and a mode‐dependent actor generates the nominal policy. Known or estimated nonlinear mode‐dependent dynamics are used in the control‐barrier‐function quadratic‐program safety filter, while generator information is used to form real‐state‐anchored virtual Bellman samples. Real online transitions and virtual samples are stored in a mode‐balanced replay buffer, which enriches mode‐wise updates without replacing the single realized trajectory. The running cost combines a bounded prescribed‐time weight with a two‐boundary barrier term, embedding deadline and safety information into value‐policy learning. The analysis combines the infinitesimal generator and Dynkin's formula between learning updates with explicit critic‐update jump bounds. The main result certifies practical prescribed‐time mean‐square uniform ultimate boundedness under an explicit generator condition based on the applied Bellman error. A nonlinear safe‐navigation simulation with unstable mode‐dependent dynamics validates deadline entry, obstacle avoidance, Markov switching, and the control‐demand tradeoff induced by different prescribed times.