Data-driven Kernel-based Predictive Control with Stability and Robustness Guarantees

Convex Offset-Free Kernelized Data-Driven Predictive Control for Nonlinear Systems

This paper presents a Kernelized Data-Driven Predictive Control (KDPC) scheme for robust, offset-free tracking of nonlinear systems. To overcome the computational burden of direct data-driven methods, we employ a hybrid framework that learns the nonlinear dynamics in a Reproducing Kernel Hilbert Space (RKHS) via joint ridge regression. A key contribution is the derivation of an analytical linearization of the kernel map, which renders the control problem a strictly convex Quadratic Program (QP) for efficient real-time implementation. We provide rigorous guarantees for recursive feasibility using terminal ingredients and establish Input-to-State Stability (ISS) with respect to the kernel approximation error. Finally, a simulation study on a Van der Pol oscillator is provided to illustrate the disturbance rejection and offset-free tracking capabilities of the proposed KDPC.

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Bilinear Koopman-Based Robust Model Predictive Control for Unknown Nonlinear Systems via Contraction Metrics

Data-driven model predictive control (MPC) using Koopman operator theory is a promising approach for constrained control of unknown nonlinear systems. While linear Koopman realizations are commonly used due to their simplicity, bilinear Koopman realizations can provide significantly higher approximation accuracy for nonlinear control systems. However, robust MPC (RMPC) formulations that account for modeling errors in bilinear Koopman realizations remain limited. This paper proposes a RMPC framework for unknown nonlinear systems with general nonlinear constraints based on data-driven bilinear Koopman realizations. A central difficulty is that finite-dimensional Koopman predictors need not preserve the manifold of valid lifted states, so multi-step prediction in lifted coordinates may leave the region where one-step error certificates apply. We address this issue by reprojecting each predicted lifted state back onto the manifold, thereby obtaining an error-aware discrete-time control-affine predictor in the original state space without impractical assumptions. For this predictor, we develop a discrete-time robust control contraction metric based homothetic tube construction, and then formulate a tube-based RMPC problem with terminal ingredients. Under the proposed formulation, we prove robust satisfaction of the original nonlinear constraints by the true closed-loop trajectory, recursive feasibility, and convergence to a neighborhood of the target state. Numerical experiments demonstrate robust stabilization of nonlinear systems and the advantages of the proposed method over existing Koopman-based RMPC approaches in terms of performance.

Data-driven predictive control of nonlinear systems using weighted regularization

This work proposes a data-driven predictive control framework for nonlinear systems that incorporates data column preferences according to their proximity to the current operating point through a weighted norm regularization, thereby localizing the predictor without discarding any data.

Data‐Driven Predictive Control for Nonlinear Systems: A Structured Prediction Approach With Kernelized Innovation Feedback

A novel nonlinear DDPC framework via a structured OP and a kernelized innovation‐based feedback mechanism is proposed, which yields lower prediction errors and better tracking performance than the existing linear and nonlinear DDPC methods.

Direct Data Driven Natural Gradient Descent for Control

This paper proposes two data-driven NGD formulations that incorporate the closed-loop covariance matrix through the Fisher Information Matrix (FIM), allowing gradient updates to be preconditioned according to the system's intrinsic uncertainty.