A multiparametric approach to accelerating ReLU neural network based model predictive control

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, rectified linear unit (ReLU) based neural networks (NN) were shown to be mixed integer linear representable, thus allowing their incorporation into mixed integer programming (MIP) frameworks. However, the resulting MIP-based MPC problems are often computationally intractable to solve 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 in itself may have a large computational cost. In this work, a novel bound tightening procedure based on a multiparametric (MP) programming formulation of the corresponding MIP reformulated MPC optimization problems is proposed. 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 two optimal control case studies: (1) A ReLU NN-based MPC of an unstable nonlinear chemostat and, (2) a ReLU NN-based MPC of a nonlinear continuously stirred tank reactor (CSTR). Significant reductions in average time of 99.96% and 91.90% are observed, for the chemostat NN based MPC and CSTR NN based MPC, respectively.