Data-Driven Scenario Optimization for Automated Controller Tuning with Probabilistic Performance Guarantees

TL;DR

This paper introduces a data-driven scenario optimization approach with probabilistic guarantees for automated controller tuning, ensuring performance bounds in complex, uncertain systems.

Contribution

It presents a novel method combining scenario theory and Bayesian optimization to provide formal performance guarantees for black-box controller tuning.

Findings

Successfully applied to nonlinear model predictive control of a semibatch reactor

Achieved distribution-free probabilistic performance bounds

Reduced computational complexity through candidate discretization

Abstract

Systematic design and verification of advanced control strategies for complex systems under uncertainty largely remains an open problem. Despite the promise of blackbox optimization methods for automated controller tuning, they generally lack formal guarantees on the solution quality, which is especially important in the control of safety-critical systems. This paper focuses on obtaining closed-loop performance guarantees for automated controller tuning, which can be formulated as a black-box optimization problem under uncertainty. We use recent advances in non-convex scenario theory to provide a distribution-free bound on the probability of the closed-loop performance measures. To mitigate the computational complexity of the data-driven scenario optimization method, we restrict ourselves to a discrete set of candidate tuning parameters. We propose to generate these candidates using constrained Bayesian optimization run multiple times from different random seed points. We apply the proposed method for tuning an economic nonlinear model predictive controller for a semibatch reactor modeled by seven highly nonlinear differential equations.