Deterministic global nonlinear model predictive control with neural networks embedded

Abstract

Nonlinear model predictive control requires the solution of nonlinear programs with potentially multiple local solutions. Here, deterministic global optimization can guarantee to find a global optimum. However, its application is currently severely limited by computational cost and requires further developments in problem formulation, optimization solvers, and computing architectures. In this work, we propose a reduced-space formulation for the global optimization of problems with recurrent neural networks (RNN) embedded, based on our recent work on feed-forward artificial neural networks embedded. The method reduces the dimensionality of the optimization problem significantly, lowering the computational cost. We implement the NMPC problem in our open-source solver MAiNGO and solve it using parallel computing on 40 cores. We demonstrate real-time capability for the illustrative van de Vusse CSTR case study. We further propose two alternatives to reduce computational time: i) reformulate the RNN model by exposing a selected state variable to the optimizer; ii) replace the RNN with a neural multi-model. In our numerical case studies each proposal results in a reduction of computational time by an order of magnitude.