Practically Predefined‐Time Adaptive Neural Control for Stochastic Nonlinear Time‐Delay Systems With State Constraints

ABSTRACT This article investigates the practically predefined‐time control problem for stochastic nonlinear systems with state constraints and both state and input delays. The coexistence of stochastic disturbances, dual delays, and state constraints poses significant challenges due to the coupling between delayed dynamics and constraint enforcement. To address the input delay, a Padé approximation combined with an auxiliary dynamic variable is employed to obtain a finite‐dimensional representation. An improved Lyapunov–Krasovskii functional is constructed to simultaneously compensate for state delays and enforce state constraints within the predefined‐time framework. Radial basis function neural networks are used to approximate unknown nonlinearities. A predefined‐time filter is incorporated into the backstepping design to ensure fast convergence of virtual control signals while avoiding the explosion of complexity and eliminating control singularities. Based on these developments, a predefined‐time adaptive controller is developed to guarantee semiglobal practically predefined‐time stability under admissible initial conditions. Comparative simulations on a single‐link robotic arm demonstrate the effectiveness and explicit time‐assignment capability of the proposed method.