Adversarially robust Bayesian optimization for efficient auto-tuning of generic control structures under uncertainty |
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Authors: | Joel A. Paulson Georgios Makrygiorgos Ali Mesbah |
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Affiliation: | 1. Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio, USA;2. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California, USA Contribution: Conceptualization (equal), Formal analysis (equal), Software (equal), Writing - original draft (equal);3. Department of Chemical and Biomolecular Engineering, University of California, Berkeley, California, USA |
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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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Keywords: | controller auto-tuning data-driven optimization model uncertainty robust Bayesian optimization |
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