Model Predictive Control: Trade-offs between Performance and Computation time

Model predictive control (MPC) uses a model of the system as a proxy to obtain multi-step predictions of the state or output variables. Thus MPC performance significantly depends on the quality of system approximation by the model. While a linear model provides a reasonable approximation of a nonlinear system over a small operating region and only requires online solution of a quadratic program (QP), the multi-step predictions can be grossly inadequate if the system trajectories cover a large operating range and the MPC performance may become unacceptable. Here, nonlinear models are necessary to provide accurate predictions. However, the online computation requires solution of a nonlinear program (NLP) instead of a QP. This trade-off between a linear and nonlinear system can be solved by use of multiple linear models, where the online optimization problem takes form of a QP but allows superior predictions than linear models. In this work, we explore the trade-off for a significantly nonlinear system namely, a continuous stirred tank reactor, by using a feed forward neural network (FFNN) as the nonlinear model for the multi-step predictions. It is seen that while the FFNN provides reasonable approximations the computation times to solve the online optimization problems are significantly higher. This trade-off motivates our future research directions of approximating the FFNN by a quasi-linear parameter varying system as a new approach to the trade-off.