Optimal design of a nonlinear control system based on new deterministic neural network scheduling

Abstract

In this paper, a new deterministic neural network scheduling is proposed to optimally design the controller of a nonlinear system. The new deterministic neural network scheduling can improve the robustness and stability of the controller design by merging the concept of scheduling based on Q-learning and the neural network algorithm. The controller design of the proposed method is online; therefore, an accurate model and plant parameters are not required. In the proposed method, a new rule for updating the Q-learning policy is used to estimate the tracking error according to the Bellman equation, and the stability of the designed controller is derived by applying graph theory and the Riccati inequality and is determined based on the Lyapunov stability. Furthermore, to illustrate the effectiveness and robustness of the proposed method, two simulated cases based on an inverted pendulum between the new deterministic neural network scheduling and a radial basis function neural network are compared. Additionally, convergences are also compared. The simulation results indicate that the controller designed by the new deterministic neural network scheduling is better than that designed by the radial basis function neural network. In addition, compared to the radial basis function neural network, the proposed method can better minimize the cost function.