Data-Knowledge-Driven Integrated Optimal Control for Multitime Scale Nonlinear Systems

In industrial processes, the optimization and control processes operate on different time scales. Neglecting the multitime scale characteristics can lead to an optimized control law that fails to guarantee the control performance of the controlled nonlinear system. To address this problem, a data-knowledge-driven multitime scale integrated optimal control (DK-MTSIOC) strategy is proposed for the nonlinear system in this article. First, a multitime scale integrated optimal control (MTSIOC) framework, including a time scale collaborative objective function, is established. Then, multitime scales of nonlinear systems are coordinated to the fast time scale to ensure real-time optimization and control. Second, to address the problem of low accuracy in predicting fast time scale model driven by the slow time scale data information, a data-knowledge-driven prediction model is introduced to predict the future dynamics of the system at the fast time scale. Furthermore, a knowledge compensation strategy is designed to supplement missing fast time scale specific information. Third, a collaborative optimization algorithm is utilized to solve the setpoints and control laws simultaneously. Besides, the convergence of the data and knowledge-driven prediction model and stability of DK-MTSIOC are proved. Finally, the proposed DK-MTSIOC is tested on a conventional nonlinear system and a benchmark example of the wastewater treatment process to validate its effectiveness.