Adaptive optimal backstepping control for strict-feedback nonlinear systems with time-varying partial output constraints

This paper investigates the optimal backstepping control strategy for strict -feedback nonlinear systems subject to input saturation and time -varying partial output constraints. Compared with the existing results on output constraints, the time -varying partial output constraint is a more general constraint that can start and end at any time during the system operation, or remain unconstrained, which can be called as output constraints occurring in a limited time interval (OCOLT). A special barrier function is embedded into the optimal performance index function to satisfy the OCOLT condition under the optimal control framework, and a shift function is introduced to address the function discontinuity caused by the OCOLT problem. Then, an auxiliary system and a disturbance observer are respectively constructed to handle the influence of the input saturation and compounded disturbances. Meanwhile, the simplified reinforcement learning algorithm, employing the identifier -critic -actor architecture, is developed to achieve the optimal control objective within the framework of the backstepping technology. Moreover, the proposed optimal control method ensures the semi -globally uniformly ultimately bounded of all signals within the closed -loop system. Finally, two simulation examples are given to further prove the effectiveness of the presented optimal control approach.