LSTM-CNN Network-Based State-Dependent ARX Modeling and Predictive Control with Application to Water Tank System

Industrial process control systems commonly exhibit features of time-varying behavior, strong coupling, and strong nonlinearity. Obtaining accurate mathematical models of these nonlinear systems and achieving satisfactory control performance is still a challenging task. In this paper, data-driven modeling techniques and deep learning methods are used to accurately capture a category of a smooth nonlinear system’s spatiotemporal features. The operating point of these systems may change over time, and their nonlinear characteristics can be locally linearized. We use a fusion of the long short-term memory (LSTM) network and convolutional neural network (CNN) to fit the coefficients of the state-dependent AutoRegressive with the eXogenous variable (ARX) model to establish the LSTM-CNN-ARX model. Compared to other models, the hybrid LSTM-CNN-ARX model is more effective in capturing the nonlinear system’s spatiotemporal characteristics due to its incorporation of the strengths of LSTM for learning temporal characteristics and CNN for capturing spatial characteristics. The model-based predictive control (MPC) strategy, namely LSTM-CNN-ARX-MPC, is developed by utilizing the model’s local linear and global nonlinear features. The control comparison experiments conducted on a water tank system show the effectiveness of the developed models and MPC methods.