Sensitivity-based scenario selection for multi-stage MPC along principal components

Abstract

The robustness, degree of conservativeness, and computational efficiency in robust multi-stage MPC are affected by scenario selection. This study explores the advantages of employing multivariate data analysis, nonlinear optimization theory, and sensitivity analysis in scenario selection to reduce conservativeness and computational burden. A novel scenario selection approach is proposed, which integrates principal component analysis and sensitivity analysis, aiming to enhance computational efficiency and mitigate conservativeness in multi-stage MPC. This method advances and extends the previously quite conservative framework of sensitivity-assisted multi-stage nonlinear MPC. Assuming that the constraints are monotonic in the parameters, the approach identifies scenarios based on sensitivities along principal components derived from analyzing large process data. The optimization problem is reformulated using the principal components to determine parameter values for critical scenarios, providing a more accurate representation of the process. The efficacy of the controller is demonstrated through various numerical examples, including a detailed thermal energy storage case study, which showcases a reduction in peak heating requirements.