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.