Predefined‐Time Command Filtered Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Systems

ABSTRACT

This paper proposes a predefined‐time command‐filtered adaptive fuzzy tracking control method applicable to stochastic nonlinear systems. Unlike existing predefined‐time stability criteria, which are exclusively formulated for deterministic systems, this paper puts forward a criterion for practical predefined‐time stability in probability, thereby extending the predefined‐time control concept to the more challenging stochastic domain. Integrating the proposed stability criterion within the backstepping framework and utilizing fuzzy logic systems (FLSs), a predefined‐time adaptive fuzzy tracking control method is developed, employing a predefined‐time command filter to resolve the classic explosion of complexity issue. This control method guarantees the convergence of the tracking error to a small neighborhood of the origin in probability within any user‐predefined time. Finally, the theoretical claims are validated through dual‐platform simulations. Comparative numerical simulations on a second‐order stochastic system demonstrate a 43.89% reduction in the overall root mean square error and significantly faster transient convergence compared to conventional fixed‐time methods, while practical feasibility is verified on a robotic manipulator.