ECCBO: An inherently safe Bayesian optimization with embedded constraint control for real-time process optimization

This paper presents a model-free real-time optimization (RTO) framework that leverages unconstrained Bayesian optimization (BO) embedded with constraint control to achieve optimal steady-state operation of process systems without the need for detailed models. Leveraging the vertical decomposition of information flow with timescale separation, this paper proposes two approaches to BO with embedded constraint controllers that simplifies model-free RTO with unknown cost and constraints, while ensuring steady-state constraint feasibility. The first approach employs constraint controllers that controls the constraints to some feasible setpoint in the fast timescale, and an unconstrained BO finds the optimal setpoints to these controllers in the slower timescale. The second approach uses constraint controllers as safety filters, where BO searchers over the RTO degrees of freedom, which can be overridden by the constraint controller when necessary to ensure steady-state constraint feasibility. By embedding constraint controllers with Bayesian optimization, both approaches ensure zero cumulative constraint violation without depending on specific assumptions about the Gaussian process model used in Bayesian optimization, making it inherently safe. The proposed scheme is demonstrated on several illustrative benchmark examples.