Machine learning-based predictive control of nonlinear time-delay systems: Closed-loop stability and input delay compensation

The purpose of this work is to study machine-learning-based model predictive control of nonlinear systems with time-delays. The proposed approach involves initially building a machine learning model (i.e., Long Short Term Memory (LSTM)) to capture the process dynamics in the absence of time delays. Then, an LSTM-based model predictive controller (MPC) is designed to stabilize the nonlinear system without time delays. Closed-loop stability results are then presented, establishing robustness of this LSTM-based MPC towards small time-delays in the states. To handle input delays, we design an LSTM-based MPC with an LSTM-based predictor that compensates for the effect of input delays. The predictor is used to predict future states using the process measurement, and then the predicted states are used to initialize the LSTM-based MPC. Stabilization of the time-delay system with both state and input delays around the steady state is achieved through the featured design. The approach is applied to a chemical process example, and its performance and robustness properties are evaluated via simulations.