A Self-Triggered Adaptive Dynamic Programming Scheme for Unknown Nonlinear Systems by Iterative Model Predictive Process

This article designs a self-triggered adaptive dynamic programming (STADP) algorithm combined with the model predictive control (MPC) mechanism to address the approximate optimal control of a nonlinear system with terminal state constraints. The MPC mechanism transforms the problem into a series of subproblems and then reduces the number of subproblems through the self-triggered mechanism (STM), thereby reducing the amount of computation. The MPC-based STADP (MSTADP) algorithm employs neural networks (NNs) to construct three key modules: the model module, the critic module, and the action module. These modules enable the identification of the unknown system, approximation of the cost function, determination of the terminal penalty, and estimation of the optimal control strategy set. Furthermore, a relaxation factor is incorporated to modulate the convergence rate of the system states online. Finally, experimental validation on two distinct systems demonstrates the algorithm’s effectiveness, and comparative experiments against the traditional HDP algorithm are performed to highlight the superiority of the proposed approach. Note to Practitioners—Industrial processes often exhibit nonlinear nonaffine behavior, posing challenges in solving Hamilton-Jacobi-Bellman (HJB) equations for nonlinear MPC. Hence, leveraging ADP to address the nonlinear HJB equations presents significant value for solving the nonlinear MPC problem. This paper presents the MSTADP algorithm to enhance predictive control in addressing unknown system dynamics within real-world industrial processes. Given the complexity of establishing mathematical models for such systems, we construct a model network using a batch of data, serving as the prediction model. Then, MSTADP mechanism is employed to determine the predictive control input under STM. Simulation experiments validate the proposed algorithm’s effectiveness, supported by a flow chart and relevant experimental parameters. The results of the experiments reveal the scheme’s strong performance.