Adaptive deep neural network optimized control for a class of nonlinear strict-feedback systems with prescribed performance

In this article, an adaptive deep neural network (DNN) optimized control strategy is developed for a class of nonlinear strict-feedback systems with prescribed performance. First, the DNN is applied to approximate the unknown function, and the weight update law is designed to reduce the mathematical challenge based on the first-order Taylor's series. Second, the optimized backstepping technique is utilized to construct virtual and actual controllers in the backstepping process to achieve the overall control optimization of the system. Next, a control strategy based on the time-varying switching function and the quartic barrier Lyapunov function is employed to achieve the prescribed performance. Then, the tracking error can converge to the prescribed accuracy within the prescribed time, and every signal within the system has a bound. Finally, the particle swarm optimization algorithm is utilized to search for the designed parameters and simulation examples to verify the effectiveness of the control strategy.