Adaptive Fault-Tolerant Control of Stochastic Nonlinear Systems With Predictable Convergence-Time Guarantee

Abstract

Guaranteeing a prescribed convergence-time bound for stochastic nonlinear systems remains challenging when actuator faults and unmodeled dynamics are present. This difficulty becomes more pronounced when both loss-of-effectiveness and bias faults occur, since they may significantly degrade the transient regulation performance of the closed-loop system. To address this issue, this paper develops an adaptive fault-tolerant stabilization scheme for a class of uncertain stochastic nonlinear systems. With the predictable convergence-time mechanism, the adaptive controller yields mean-square practical fixed-time stability, and the corresponding settling-time estimate is explicitly tunable. A Lyapunov-based analysis together with a time-varying gain technique is employed to establish sufficient conditions ensuring boundedness of all closed-loop signals and convergence of the system states within the prescribed convergence-time bound. Moreover, auxiliary normalized performance indices are introduced in the post-processing stage to quantify the transient regulation burden caused by actuator faults. Finally, a stochastic nonlinear system and a quadrotor attitude subsystem are used for simulation validation, covering representative composite-fault cases and four actuator fault scenarios. The results illustrate the performance and robustness of the proposed strategy. Note to Practitioners—In safety-critical automation applications, uncrewed aerial vehicles (UAVs), robotic platforms, and intelligent manufacturing equipment are often exposed to random disturbances, actuator degradations, and modeling inaccuracies. These factors may degrade control performance and prolong the recovery process after faults occur. In practice, engineers often require not only fault tolerance and robustness, but also predictable recovery within a specified time horizon. In quadrotor operations, wind gusts, actuator degradation, and payload-induced modeling uncertainties may arise simultaneously, making predictable recovery within a specified time horizon difficult to achieve. In contrast to conventional designs with settling behavior affected by tuning gains and operating scenarios, this method lets practitioners prescribe the desired recovery-time bound during controller design. The framework can accommodate both loss-of-effectiveness faults and bias faults without requiring precise fault information. It is suitable for safety-critical automation systems requiring reliable operation under uncertainty. Practitioners should select the time bound and adaptation gains by balancing response speed and control effort.