Predefined time convergence guaranteed performance control for uncertain systems based on reinforcement learning

Abstract

The prescribed performance control method (PPCM) is commonly employed to ensure the guaranteed performance control of non-linear systems. However, traditional approaches suffer from certain drawbacks, such as the dependence of parameter settings for the performance constraint function on the initial tracking error value and the inability to specify the convergence time of tracking error according to engineering requirements. This paper focuses on designing a fault tolerant control strategy with prescribed convergence time and prescribed transient performance for uncertain systems, considering parameter perturbance, actuator faults, and unknown initial states. Firstly, we introduce an error conversion function that transforms the tracking error with any initial value into a new error variable starting from zero. This resolves the issue of depending on the initial value of tracking error in setting parameters for the performance constraint function in prescribed performance control methods. Subsequently, we derive a novel Lyapunov stability criterion for predefined time (PDT) convergence and design a fault-tolerant control strategy using backstepping control method while ensuring prescribed convergence time and prescribed performance. In this approach, we propose a new online reinforcement learning intelligent algorithm to estimate compound interference caused by actuator faults, control saturation constraint increment, system parameter perturbation, and external interference. The theoretical proof establishes predefined time convergence of the closed-loop system. Finally, numerical simulations are conducted on industrial robots with actuator faults to validate the effectiveness of our designed control strategy.