The closed-loop performance of model predictive controllers (MPCs) is sensitive to the choice of prediction models, controller formulation, and tuning parameters. However, prediction models are typically optimized for prediction accuracy instead of performance, and MPC tuning is typically done manually to satisfy (probabilistic) constraints. In this work, we demonstrate a general approach for automating the tuning of MPC under uncertainty. In particular, we formulate the automated tuning problem as a constrained black-box optimization problem that can be tackled with derivative-free optimization. We rely on a constrained variant of Bayesian optimization (BO) to solve the MPC tuning problem that can directly handle noisy and expensive-to-evaluate functions. The benefits of the proposed automated tuning approach are demonstrated on a benchmark continuously stirred tank reactor example.
Many real‐world design problems involve optimization of expensive black‐box functions. Bayesian optimization (BO) is a promising approach for solving such challenging problems using probabilistic surrogate models to systematically tradeoff between exploitation and exploration of the design space. Although BO is often applied to unconstrained problems, it has recently been extended to the constrained setting. Current constrained BO methods, however, cannot identify solutions that are robust to unavoidable uncertainties. In this article, we propose a robust constrained BO method, constrained adversarially robust Bayesian optimization (CARBO), that addresses this challenge by jointly modeling the effect of the design variables and uncertainties on the unknown functions. Using exact penalty functions, we establish a bound on the number of CARBO iterations required to find a near‐global robust solution and provide a rigorous proof of convergence. The advantages of CARBO are demonstrated on two case studies including a non‐convex benchmark problem and a realistic bubble column reactor design problem.
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