(711b) A Multiparametric Approach to Solving NN Constrained Model Predictive Control Problems Effectively

Model Predictive Control (MPC) is a wide spread advanced process control methodology for optimization based control of multi-input and multi-output processes systems. Typically, a surrogate model of the process dynamics is utilized to predict the future states of a process as a function of input actions and an initial state. The predictive model is often a linear model, such as a state space model, due to the computational burden of the resulting optimization problem when utilizing nonlinear models. Recently, certain classes of neural networks (NN) were shown to be mixed integer linear representable, thus allowing their incorporation into mixed integer programming solvers and frameworks. However, the resulting NN-based MPC problems are often computationally intractable to solve to provable optimality in real-time. The computational intractability of the reformulated NN-based optimization models is typically addressed in the literature by applying some form of bounds tightening approach. However, this procedure in itself may have a large computational cost.

In this work, we propose a novel bound tightening procedure based on a multiparametric (MP) programming formulation of the corresponding NN reformulated MPC optimization problems. Which tightening only needs to be computed and applied once-and-offline, thereby significantly improving the computational performance of the MPC in real-time. Some aspects of the effect of regularization during NN regression on the computational difficulty of these optimization problems are also investigated in conjunction with the proposed a priori bounds-tightening approach. The proposed method is compared to the base case without the parametric tightening procedure, as well as NN regularization through and optimal control case study of an unstable nonlinear chemostat.