Optimised finite-time control of stochastic nonlinear systems with guaranteed prescribed performance and singularity avoidance

This study investigates an adaptive neural network (NN) finite-time optimal control issue for a class of stochastic nonlinear systems with full-state tracking error constraints. A prescribed performance function (PPF)-based error transformation technique is developed, which enforces the tracking error constraints and guarantees both transient and steady-state performance. Then, under the architecture of the identifier-actor-critic, and combined with backstepping technique, the virtual and actual optimal controllers are designed. To address the “singularity” problem inherent in the backstepping design framework, an adaptive NN finite-time control method is proposed. Furthermore, the dynamic surface control (DSC) mechanism is integrated within the control scheme to overcome the computational “complexity explosion” issue in the backstepping control design process. Based on finite-time stability criteria, it is proven that all closed-loop signals remain bounded under the proposed optimal controller. Meanwhile, it guarantees that tracking errors converge rapidly within prescribed bounds. Ultimately, both numerical and practical systems further validate the practicality and effectiveness of the proposed approach.