Predefined-Time and Predefined-Accuracy Sliding Mode Control With Unknown Bound Uncertainties

This article presents an adaptive neural network-based sliding mode control (SMC) strategy aimed at achieving predefined-time and predefined-accuracy (PTPA) convergence of tracking errors. Notably, the proposed approach does not require prior knowledge of the upper bounds of uncertainties or the control direction. To ensure PTPA convergence and prevent singularity, a novel piecewise PTPA sliding mode manifold incorporating a nonlinear compensating term is introduced. This compensating term is specifically designed to address the bounded sliding-mode errors induced by model uncertainties and external disturbances. Furthermore, by enforcing a PTPA constraint on the sliding mode function and utilizing the Nussbaum function, the system states can converge to a predefined neighborhood of the sliding mode surface within a predefined time. An adaptive neural network-based PTPA SMC law is then developed, eliminating discontinuous terms and effectively mitigating the chattering issue. The proposed control scheme is rigorously proven to achieve PTPA convergence and asymptotic convergence. The efficacy of the designed control strategy is validated through two numerical examples, demonstrating its superior performance.