Data-Driven Multimodel Predictive Control for Multirate Sampled-Data Nonlinear Systems

Abstract

This paper is concerned with the asynchronous control problem of multi-rate sampled-data nonlinear systems. To solve this problem, the data-driven multi-model predictive control (DMMPC) strategy is proposed. First, a multi-model predictive control structure is designed such that each state variable of the multi-rate sampled-data nonlinear system can be controlled synchronously at all sampling instants. In this structure, the fuzzy neural network (FNN) is introduced to build the multi-model. Then, the prediction outputs of each state variable at all sampling instants are obtained to provide control information for the controller. Specially, the objective function with adaptive weight matrix (AWM) is designed to reduce the influence of the prediction error caused by nonlinear fitting on control performance. Then, the optimal control laws are calculated to improve the control precision. Finally, the convergence and stability of DMMPC are proved in detail. The numerical example and industrial application reveal that the proposed DMMPC can obtain considerable control performance for the multi-rate sampled-data nonlinear systems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The asynchronous control problem of the multi-rate sampled-data nonlinear system (MRSNS) may degrade the operation performance of closed-loop system. In this paper, a data-driven multi-model predictive control (DMMPC) strategy is designed for MRSNS without mechanism model. The strategy mainly consists of three parts: First, a multi-model prediction structure based on fuzzy neural network (FNN) is established to obtain the prediction output of all variables at each sampling point. The parameters of FNNs are corrected at each sampling point to ensure prediction accuracy. Second, an objective function with an adaptive weight matrix (AWM) is designed to compute the control law, in which AWM is used to reduce the influence of prediction error on control performance. Third, the effectiveness of DMMPC is verified by a numerical example and an industrial application of the wastewater treatment process. The experimental results show that DMMPC can achieve satisfied operation performance in control accuracy.