Model-free real-time optimization of process systems using safe Bayesian optimization

Conventional real-time optimization (RTO) requires detailed process models, which may be challenging or expensive to obtain. Model-free RTO methods are an attractive alternative to circumvent the challenge of developing accurate models. Most model-free RTO methods are based on estimating the steady-state cost gradient with respect to the decision variables and driving the estimated gradient to zero using integral action. However, accurate gradient estimation requires clear time scale separation from the plant dynamics, such that the dynamic plant can be assumed to be a static map. For processes with long settling times, this can lead to prohibitively slow convergence to the optimum. To avoid the need to estimate the cost gradients from the measurement, this article uses Bayesian optimization, which is a zeroth order black-box optimization framework. In particular, this article uses a safe Bayesian optimization based on interior point methods to ensure that the setpoints computed by the model-free steady-state RTO layer are guaranteed to be feasible with high probability (i.e., the safety-critical constraints will not be violated at steady-state). The proposed method can thus be seen as a model-free variant of the conventional two-step steady-state RTO framework (with steady-state detection), which is demonstrated on a benchmark Williams-Otto reactor example.