Learning Economic Model Predictive Control via Clustering and Kernel-Based Lipschitz Regression

TL;DR

This paper introduces a novel learning economic model predictive control method for uncertain nonlinear systems, utilizing clustering and kernel-based Lipschitz regression to accurately learn unknown dynamics and ensure system stability.

Contribution

It develops a fast Lipschitz regression approach combining clustering and kernel methods, with new error bounds and a robust constraint strategy for improved control of uncertain nonlinear systems.

Findings

Effective learning of unknown dynamics demonstrated in simulations.

Guaranteed recursive feasibility and input-to-state stability.

Validated on a numerical example and a stirred tank reactor.

Abstract

This paper presents a novel learning economic model predictive control scheme for uncertain nonlinear systems subject to input and state constraints and unknown dynamics. We design a fast and accurate Lipschitz regression method using input and output data that combines clustering and kernel regression to learn the unknown dynamics. In each cluster, the parallel convex optimization problems are solved to estimate the kernel weights and reduce the Lipschitz constant of the predictor, hence limiting the error propagation in the prediction horizon. We derive the two different bounds of learning errors in deterministic and probabilistic forms and customize a new robust constraint-tightening strategy for the discontinuous predictor. Then, the learning economic model predictive control algorithm is formulated by introducing a stabilized optimization problem to construct a Lyapunov function. Sufficient conditions are derived to ensure the recursive feasibility and input-to-state stability of the closed-loop system. The effectiveness of the proposed algorithm is verified by simulations of a numerical example and a continuously stirred tank reactor.