Adaptive optimized backstepping tracking control for full‐state constrained nonlinear strict‐feedback systems without using barrier Lyapunov function method

Abstract In this article, the problem of adaptive optimal tracking control is studied for nonlinear strict‐feedback systems. While not directly measurable, the states of these systems are subject to both time‐varying and asymmetric constraints. Bypassing the conventional barrier Lyapunov function method, the constrained system is transformed into its unconstrained counterpart, thereby obviating the need for feasibility conditions. A specially designed reinforcement learning (RL) algorithm, featuring an observer‐critic‐actor architecture, is deployed in an adaptive optimal control scheme to ensure the stabilization of the converted unconstrained system. Within this architecture, the observer estimates the unmeasurable system states, the critic evaluates the control performance, and the actor executes the control actions. Furthermore, enhancements to the RL algorithm lead to relaxed conditions of persistent excitation, and the design methodology for the observer overcomes the restrictions imposed by the Hurwitz equation. The Lyapunov stability theorem is applied for two primary purposes: to ascertain the boundedness of all signals within the closed‐loop system, and to ensure the accuracy of the output signal in tracking the desired reference trajectory. Finally, numerical and practical simulations are provided to corroborate the effectiveness of the proposed control strategy.