A New Componentwise Hölder Regression Method for Shrink-Horizon Economic Model Predictive Control.

Abstract

This article proposes a novel learning-based Shrink-Horizon Economic Model Predictive Control (SHEMPC) algorithm for constrained nonlinear systems with unknown dynamics and additive disturbances. By combining data clustering and kernel techniques, a componentwise Hölder regression algorithm is customized to construct an accurate and sparse dynamics predictor. The kernel weights and Hölder matrices within each cluster are determined using a tailored Block Coordinate Descent (BCD) optimization method. Then, two error bounds of the regression-based predictor are estimated a priori for the design of SHEMPC. Next, by integrating the customized constraint-tightening method of the predictor, the SHEMPC algorithm is formulated as two finite-horizon receding optimization problems solved iteratively. The algorithm enables a flexible trade-off among economic performance, stability, and online computational burden via simple parameter adjustments. Moreover, some mild assumptions are derived to ensure the feasibility and Input-to-State Stability (ISS) of the closed-loop system as well as smoothness and prediction complexity of the predictor. The performance and merits of the proposed algorithm are illustrated through a numerical example and a Continuously Stirred Tank Reactor (CSTR) simulation.