Adaptive fixed-time optimal backstepping control using reinforcement learning for a class of nonlinear systems

This paper focuses on the problem of adaptive fixed-time optimal control for strict-feedback nonlinear systems. To attain optimal control, both virtual and actual controllers are devised utilizing an actor–critic framework, which serves to approximate the uncertain component inherent. The updating law is derived from the negative gradient of a simple positive function, rather than the Bellman residual error, thereby significantly simplifying the optimal control implementation. Since the fixed-time controller is constructed using fractional powers, the system signals can reach convergence states within the setting time which is not affected by the initial conditions. A first-order filter is introduced to replace the virtual controller with its output, thereby reducing the computational complexity. Hence, the proposed control scheme not only achieves optimal control but also simplifies the algorithm. Furthermore, the Lyapunov stability theorem is leveraged to ensure the control performance, and two simulation experiments are conducted to substantiate the efficacy of the control algorithm.