Online Critic Dynamic Programming Based Optimal Control for Three-Shaft Web Machine Systems

This article carries out research into an adaptive optimal controller for three-shaft web machine systems to simultaneously regulate tracking problems and cost optimization. First of all, we introduce a tracking error model system by taking the backstepping-based technique to serve the controller design purpose. After that, a critic dynamic programming scheme is proposed that is able to approximate the solution of the Hamilton-Jacobi-Bellman equation. Our scheme just employs a neural network for approximation tasks, thereby evidencing the relevance and feasibility of the designed controller for real-life web machine systems. The convergence of critic weights and system stability is considered through Lyapunov stability theory. Finally, compared simulation results are given to validate the effectiveness of the control algorithm.