Safe Real-Time Optimization using Multi-Fidelity Gaussian Processes

TL;DR

This paper introduces a real-time optimization method that combines multi-fidelity Gaussian processes with derivative-free optimization to effectively handle system-model mismatch and ensure safety in uncertain processes.

Contribution

It integrates multi-fidelity Gaussian processes within a Bayesian optimization framework to improve real-time system optimization with uncertainty quantification.

Findings

Effective handling of system-model mismatch.

Real-time uncertainty quantification enabled.

Successful application to a photobioreactor case study.

Abstract

This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes within a Bayesian optimization framework. The proposed scheme uses two Gaussian processes for the stochastic system, one emulates the (known) process model, and another, the true system through measurements. In this way, low fidelity samples can be obtained via a model, while high fidelity samples are obtained through measurements of the system. This framework captures the system's behavior in a non-parametric fashion while driving exploration through acquisition functions. The benefit of using a Gaussian process to represent the system is the ability to perform uncertainty quantification in real-time and allow for chance constraints to be satisfied with high confidence. This results in a practical approach that is illustrated in numerical case studies, including a semi-batch photobioreactor optimization problem.