Adversarially robust Bayesian optimization for efficient auto‐tuning of generic control structures under uncertainty

Abstract

The performance of optimization‐ and learning‐based controllers critically depends on the selection of several tuning parameters that can affect the closed‐loop control performance and constraint satisfaction in highly nonlinear and nonconvex ways. Due to the black‐box nature of the relationship between tuning parameters and general closed‐loop performance measures, there has been a significant interest in automatic calibration (i.e., auto‐tuning) of complex control structures using derivative‐free optimization methods, including Bayesian optimization (BO) that can handle expensive unknown cost functions. Nevertheless, an open challenge when applying BO to auto‐tuning is how to effectively deal with uncertainties in the closed‐loop system that cannot be attributed to a lumped, small‐scale noise term. This article addresses this challenge by developing an adversarially robust BO (ARBO) method that is particularly suited to auto‐tuning problems with significant time‐invariant uncertainties in an expensive system model used for closed‐loop simulations. ARBO relies on a Gaussian process model that jointly describes the effect of the tuning parameters and uncertainties on the closed‐loop performance. From this joint Gaussian process model, ARBO uses an alternating confidence‐bound procedure to simultaneously select the next candidate tuning and uncertainty realizations, implying only one expensive closed‐loop simulation is needed at each iteration. The advantages of ARBO are demonstrated on two case studies, including an illustrative problem and auto‐tuning of a nonlinear model predictive controller using a benchmark bioreactor problem.

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