Deep Learning-Based State-Dependent ARX Modeling and Predictive Control of Nonlinear Systems

For many practical industrial objects with time-varying operating points, strong nonlinearity, and difficulty in obtaining analytical models, the data-driven identification method is usually used to model such nonlinear systems. However, it is difficult for traditional modeling algorithms to effectively extract the dynamic characteristics of nonlinear systems from data and obtain accurate mathematical models. In this paper, we consider using the deep learning network combined with the state-dependent exogenous variable autoregressive (SD-ARX) model framework to build the nonlinear system model, so as to effectively and accurately learn the space-time characteristics of the nonlinear system from the sample data. Based on the idea, the hybrid models, i.e., the RNN-ARX model, CNN-ARX model, and RNN-CNN-ARX model are built, which use recurrent neural networks (RNN), convolutional neural networks (CNN) and their combination to fit the function-type coefficients of SD-ARX model, respectively. SD-ARX model based on deep learning has the advantages of local linearity and global nonlinearity. Compared with the other two models, the RNN-CNN-ARX model has a stronger ability to extract the multidimensional spatiotemporal dynamic characteristics of nonlinear systems, because it combines the advantages of RNN in mining temporal features and CNN in extracting spatial features. According to the structural characteristics of these models, three model-based predictive control (MPC) strategies are designed, i.e., RNN-ARX-MPC, CNN-ARX-MPC, and RNN-CNN-ARX-MPC. The real-time control comparative experiment on an actual multi-water-tank object shows that the proposed modeling and MPC method is feasible and effective for the modeling and predictive control of the nonlinear system.