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

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

In this paper, we provide a theoretical analysis of the closed-loop properties of a data-driven kernel-based predictive control (DDKPC) scheme developed solely from input-output data. The proposed formulation integrates a robust data-driven predictive control framework with a multi-step predictor for nonlinear systems constructed via kernel-based methods. This predictor implicitly captures the system's nonlinear behavior using the representer theorem. For the nominal case with noise-free data, we prove that the DDKPC scheme guarantees recursive feasibility and closed-loop stability, provided that the prediction horizon is sufficiently long and the kernel representation error is sufficiently small. To facilitate real-time implementation, we introduce a penalty relaxation formulation to alleviate the computational burden inherently caused by nonconvex implicit constraints. Furthermore, the framework is robustified against measurement noise by aggregating the representation mismatch and the bounded noise into a unified uncertainty bound. Finally, we extend the DDKPC framework to slowly time-varying nonlinear systems by periodically reconstructing the kernel predictor from a fixed-budget online dictionary managed by the approximate linear dependency (ALD) criterion. Under suitable conditions on the rate of variation of the input-output evolution and the online prediction error, recursive feasibility and practical closed-loop stability are preserved. The effectiveness of the proposed approach is illustrated through numerical examples.

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

Data‐driven predictive control (DDPC) methods have received increasing interest and gained exceptional success in linear systems. However, extending DDPC to nonlinear systems remains a challenging task, primarily due to the difficulty in balancing the complexity of the output predictor (OP) with generalization capability, and the inability of a static OP to cope with real‐time unmodeled dynamics. In this paper, we propose a novel nonlinear DDPC framework via a structured OP and a kernelized innovation‐based feedback mechanism. To effectively capture nonlinear dynamics from data, we first design a new structured predictor that consists of a nominal linear term for capturing coarse‐grained linear relations and a nonlinear term established in the reproducing kernel Hilbert space (RKHS), capturing fine‐grained nonlinearity. To further enhance robustness against unmodeled dynamics and disturbance, a kernelized feedback mechanism is designed to correct predicted outputs based on real‐time innovation sequences. A tailored heuristic algorithm based on alternating minimization is designed to effectively solve the data‐driven parameter estimation problem. By applying the data‐driven OP in the control regime, a new DDPC method for nonlinear systems is derived. Comprehensive studies on a nonlinear numerical example and a robotic manipulator demonstrate that the proposed method yields lower prediction errors and better tracking performance than the existing linear and nonlinear DDPC methods.

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

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.

Inverse optimal control of general nonlinear systems based on adaptive dynamic programming