Asymmetric time-varying integral barrier Lyapunov function based adaptive optimal control for nonlinear systems with dynamic state constraints

This paper investigates the issue of adaptive optimal tracking control for nonlinear systems with dynamic state constraints. An asymmetric time-varying integral barrier Lyapunov function (ATIBLF) based integral reinforcement learning (IRL) control algorithm with an actor–critic structure is first proposed. The ATIBLF items are appropriately arranged in every step of the optimized backstepping control design to ensure that the dynamic full-state constraints are never violated. Thus, optimal virtual/actual control in every backstepping subsystem is decomposed with ATIBLF items and also with an adaptive optimized item. Meanwhile, neural networks are used to approximate the gradient value functions. According to the Lyapunov stability theorem, the boundedness of all signals of the closed-loop system is proved, and the proposed control scheme ensures that the system states are within predefined compact sets. Finally, the effectiveness of the proposed control approach is validated by simulations.