Adaptive Neural Optimal Control of a Robot Manipulator with Time-Varying State Constraints

This study explores the problem of adaptive optimal tracking control for a robot manipulator with time-varying state constraints. An adaptive neural optimal control scheme is proposed using an asymmetric time-varying integral barrier Lyapunov function (ATIBLF). In order to address the challenges associated with solving the Hamilton-Jacobi-Bellman equation for nonlinear robot systems, the adaptive optimal tracking controller is designed within the framework of “actor-critic”. The ATIBLF terms are appropriately incorporated at each step of the optimized backstepping control design to ensure that the time-varying state constraints are never violated. Stability analysis demonstrates that all closed-loop signals of the robot system remain bounded and do not violate the time-varying state constraints. Simulations are conducted to validate the effectiveness of the proposed control method.