Safety-Aware Optimal Tracking Control of Stochastic Systems with Obstacle Avoidance Via Adaptive Dynamic Programming

Safe trajectory tracking for nonlinear stochastic systems operating in obstacle-cluttered environments remains a significant challenge, as random disturbances and obstacle-induced constraints can simultaneously degrade tracking accuracy and threaten system safety. To overcome this issue, this article develops a safety-aware optimal tracking control framework that integrates stochastic control barrier functions (CBFs) with adaptive dynamic programming (ADP) for obstacle avoidance. To ensure safety, a logarithmic-type stochastic CBF is constructed to enforce obstacle-avoidance constraints, and theoretical guarantees are provided for the stochastic forward invariance (SFI) of the safe set. Furthermore, based on the integral reinforcement learning (RL) framework, an ADP algorithm is developed to relax the need for system dynamics. A critic-only neural network (NN) scheme is employed to approximate the solution of the Hamilton-Jacobi-Bellman (HJB) equation, with a fixed-time weight update rule established to guarantee convergence independent of initial conditions. Meanwhile, an experience replay mechanism is incorporated to relax the persistent excitation condition. It is further shown that the estimation error of the NN weights is fixed-time stable (FxTS). Finally, simulation results demonstrate that the designed method achieves optimal trajectory tracking while ensuring safety under stochastic dynamics, even in scenarios involving multiple obstacles.