Reinforcement learning based adaptive optimal control for constrained nonlinear system via a novel state-dependent transformation

Existing schemes for state-constrained systems either impose feasibility conditions or ignore the optimality. In this article, an adaptive optimal control scheme for the strict-feedback nonlinear system is proposed, which benefits from two design steps. Firstly, a novel nonlinear state-dependent function (NSDF) is formulated to equivalently transform the system into a non-constrained one to deal with state constraints without the requirements on feasibility conditions. Secondly, an adaptive optimal control scheme is designed for the non-constrained system, in which reinforcement learning (RL) is utilized to yield the optimal controller in each designing procedure. Updating rules of the actor and critic neural network are driven by the modified adaptive laws, used to approximate the optimal virtual and actual controllers. It is proved that all the signals in the closed-loop system are bounded and the output tracking error converges to an adjustable neighborhood of the origin not affected by the proposed NSDF. Two simulation examples are presented illustrating the effectiveness of the proposed scheme.