Simulation-based Integrated Design and Control with Embedded Mixed-Integer MPC using Constrained Bayesian Optimization

We present a black-box optimization approach for the integration of design and control of constrained nonlinear systems under uncertainty. The problems of interest are difficult to solve since the dynamics and uncertainties occur on much shorter timescales than the process lifetime, the uncertainties are described by continuous random variables with high variance, and key operational decisions are modeled with a mixture of discrete and continuous variables. Instead of aggressively simplifying the number of operational periods and uncertainty scenarios to improve tractability of the problem, we are interested in developing a simulation-based optimization strategy by employing a high-quality decision rule that maps information measured online to the control inputs. Due to the inclusion of discrete scheduling decisions, we focus on a variant of model predictive control that can handle both continuous and discrete variables. We use a sample average approximation at every iteration to approximate the expected operating costs and constraints appearing in the main problem. Since the black-box optimizer handles noisy objective and constraint evaluations, it can mitigate errors introduced by considering only a finite number of samples. The advantages of the proposed method compared to alternative sequential design and control schemes are demonstrated on the design of a building cooling system under uncertain weather and demand conditions.