Data-Efficient Koopman Tracking MPC for Nonlinear Systems: A Kernel-Based Approach

Abstract

This paper presents a data-efficient Koopman-based tracking model predictive control (MPC) scheme for nonlinear systems. Linear surrogate models are constructed online via a kernel extended dynamic mode decomposition (EDMD) framework in a reproducing kernel Hilbert space (RKHS), for which a proportional approximation error bound is established. The proposed online mechanism restricts model learning to a one-dimensional system trajectory, thereby improving data efficiency by avoiding the incorporation of redundant data. Despite the online construction of the surrogate models, the proposed scheme remains computationally tractable and suitable for real-time implementation. Furthermore, the practical exponential stability of the optimal reachable equilibrium (ORE) associated with a given reference signal is rigorously established. The proposed method is further evaluated via a numerical example. Note to Practitioners—Many industrial systems exhibit nonlinear dynamics that are difficult to model accurately using first-principles approaches, limiting the applicability of conventional MPC. This paper proposes a data-efficient Koopman-based tracking MPC method that constructs linear surrogate models online using data along the system trajectory, avoiding extensive offline identification. The approach captures nonlinear behavior while retaining the computational efficiency of linear MPC, enabling real-time implementation. It is particularly suitable for systems with limited data or partially unknown dynamics.