Nonlinear model predictive control algorithm with iterative nonlinear prediction and linearization for long short-term memory network models

Abstract

In this paper, a practical nonlinear model predictive control with iterative nonlinear prediction and linearization is proposed, considering a long short-term memory (LSTM) artificial neural network (PNMPCi-LSTM) as process model for making the predictions. The prediction model is divided into two portions, the base output prediction, obtained with the LSTM nonlinear model, and the incremental output prediction, obtained using a linearized version of the LSTM model. The base response and the dynamic matrix of the system, which is obtained using the linearized version, are used to find an optimal control effort by solving a quadratic programming problem. This procedure is performed iteratively by updating the base input with the candidate control effort until the incremental response term is small enough compared with the base response term. The advantages of the proposed method in terms of performance and computing times are illustrated using the control of a simulated nonlinear neutralization reactor. For the evaluated case study, the results show that by using the proposed iterative procedure the closed-loop performance measured using the integral absolute error is improved by 8% for a setpoint tracking scenario while keeping the computation times within reasonable levels. In addition, the results support the idea that the proposed PNMPCi-LSTM is an alternative to implement a nonlinear MPC with reasonable computation times.