Fuzzy Control Based on Reinforcement Learning and Subsystem Error Derivatives for Strict-Feedback Systems With an Observer

In this article, a novel optimized fuzzy adaptive control method based on tracking error derivatives of subsystems is proposed for strict-feedback systems with unmeasurable states. A cost function based on the tracking error derivative is used. It not only solves the problem that the traditional input quadratic cost function at the infinite time is unbounded, but also solves the problem that the optimal control input derived from the cost function with exponential discount factor cannot make the error asymptotically stable. Considering the case where the states are unmeasurable, a fuzzy state observer is designed that removes the restriction of the Hurwitz equation for the gain parameters. Based on reinforcement learning, the observer, and error derivative cost function, an improved optimized backstepping control method is given. Using observed information and actor-critic structure to train fuzzy logic systems online, the control inputs are obtained to achieve approximate optimal control. Finally, all closed-loop signals are proved to be bounded by the Lyapunov method, and the effectiveness and advantages of the proposed algorithm are verified through two examples.