We present a novel approach that enables the solution of nonlinear model predictive control with integer decisions in real time even when when the model is subject to many uncertainties. Our approach tightly integrates three different ideas. First, we use combinatorial integral approximation as a powerful heuristic to approximate the mixed-integer nonlinear problems with two nonlinear problems. Next, we formulate a scenario tree formulation to deal with uncertain parameters. To tackle the large number of uncertainties, we propose a scenario decomposition method to solve each scenario problem in parallel. We integrate the combinatorial approximation within this scenario decomposition method to provide a method for uncertain parameters within mixed-integer model predictive control. This method leads to many smaller optimization problems that can be solved in parallel. As the third idea, we propose the use of learned iterative solvers, as opposed to traditional numerical solvers, to solve each subproblem. This methodology can be massively parallelized by evaluating neural networks on powerful GPUs. As a result, the proposed approach leads to an order of magnitude faster solutions when compared to a solution of the entire robust problem with a traditional numerical solver, as well as to improved accuracy in comparison to a supervised learning approach. This is illustrated in the simulation example of an uncertain nonlinear reactor with mixed-integer decisions. • Integration of combinatorial integral approximation into robust multi-stage MPC. • Self-supervised learning approach for GPU-based acceleration of the MPC problem. • Real-time applicability for mixed-integer systems with large amounts of uncertainties.
Adamek et al. (Tue,) studied this question.