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

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

A theoretical analysis of the closed-loop properties of a data-driven kernel-based predictive control (DDKPC) scheme developed solely from input-output data proves that the DDKPC scheme guarantees recursive feasibility and closed-loop stability.

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.

A subspace approach to data-driven predictive control for linear parameter-varying systems

This paper presents a subspace data-driven predictive control method for linear parameter-varying (LPV) systems. Starting from an affine LPV state-space model in innovation form, we derive a multi-step predictor that separates the effects of past data, future inputs, scheduling trajectories, and innovations. By projecting this representation onto the row span of lifted input-output-scheduling data, we obtain an asymptotically unbiased data-driven predictor that can be embedded directly in a receding-horizon control problem, without explicitly identifying an LPV model. To make the resulting LPV data-driven predictive control (DDPC) formulation tractable, we introduce an LPV extension of $\gamma$-DDPC based on an LQ factorization. This formulation fixes the number of online decision variables independently of the length of the dataset. A reduced-order predictor is then proposed to curb the exponential growth of scheduling-dependent regressors, which also relaxes the persistence-of-excitation condition. Simulation studies, including an unbalanced-disk example, show that the proposed controller achieves good tracking performance and, compared to existing LPV DDPC schemes, achieves better robustness to measurement noise and reduced computational cost, making multi-step LPV DDPC practically deployable, even with longer past horizons.

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.

Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecasting

Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging. Existing approaches that explicitly model system dynamics typically rely on linear assumptions or Koopman-based linearizations, which may inadequately capture complex nonlinear behaviors and lead to error accumulation in long-horizon prediction. To address this limitation, we propose the Neural Bilinear Dynamical Model (NBDM), which models nonlinear system dynamics through a bilinear latent dynamical formulation. Specifically, NBDM leverages Koopman theory to lift the original nonlinear dynamics into a higher-dimensional latent space, where a bilinear dynamical model is constructed to characterize state evolution. To mitigate the approximation error introduced by bilinear representations, we further incorporate a parameterized error compensation term. Within this formulation, control inputs are explicitly integrated into the dynamics, using auxiliary variables when available and learned feedback signals otherwise. To handle scenarios with missing control inputs, we design a memory-enhanced controller that infers latent controls through multiplicative interactions between historical states and control signals. Experiments on five real-world datasets demonstrate that NBDM consistently outperforms competitive baselines in both given-control and missing-control settings, particularly for multi-step and long-horizon forecasting.

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