Robust Offset-free Kernelized Data-Driven Predictive Control for Nonlinear Systems

TL;DR

This paper introduces a kernelized data-driven predictive control method that achieves robust, offset-free tracking of nonlinear systems with real-time efficiency, stability guarantees, and disturbance rejection.

Contribution

It presents a hybrid approach combining kernel ridge regression and analytical linearization to enable offset-free, robust control of nonlinear systems in a computationally efficient manner.

Findings

Successfully rejects unmeasured disturbances in experiments.

Eliminates steady-state errors in nonlinear system control.

Outperforms standard model-based controllers in validation.

Abstract

This paper proposes a novel Kernelized Data-Driven Predictive Control (KDPC) scheme for robust, offset-free tracking of nonlinear systems. Our computationally efficient hybrid approach separates the prediction: (1) kernel ridge regression learns the nonlinear map from past trajectories, and (2) analytical linearization of the kernel map approximates the effect of future inputs. This linearization is key, allowing the controller to be formulated as a standard Quadratic Program (QP) for efficient real-time implementation. Offset-free tracking is inherently achieved by using input increments. We provide theoretical guarantees for recursive feasibility and asymptotic stability. The algorithm is validated on a nonlinear Van der Pol oscillator, where it successfully rejects unmeasured disturbances and eliminates steady-state errors, outperforming a standard model-based controller.