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.
Abstract
Data-driven control methods, like Data-enabled Predictive Control (DeePC), are often formulated for linear systems, where the principle of superposition allows global system behavior to be inferred from locally collected data through Willems'fundamental lemma. This principle does not hold for nonlinear systems, whose dynamics may vary across operating regions. We propose 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. We show how the proposed weighting scheme induces operating point-dependent data prioritization and ensures a well-posed optimization problem. A numerical study on a nonlinear two-tank system demonstrates that the proposed method matches or outperforms hard data-selection schemes while retaining the full data matrix and its rank, thereby guaranteeing feasibility.
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.
Wenjie Liu, Yifei Li, Gang Wang et al.· 0 citations
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.
Mahmood Mazare, Hossein Ramezani· 2026 6th International Confe...· 0 citations
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.
Federico Porcari, C. Verhoek, V. Breschi et al.· 0 citations
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.
Yibo Wang, Yunxiang Ma, Tao Liu et al.· International Journal of Rob...· 0 citations
Indirect data-driven predictive control methods often suffer under process noise and data scarcity. This paper introduces Projection-Regularized Predictive Control (PRPC), retaining the fundamental-lemma weight vector via a regularized projection analytically condensed into an efficient, fixed-dimension covariance update. A rigorous bias--variance analysis proves PRPC strictly reduces prediction error under process noise (errors-in-variables) and structural rank deficiencies compared to unregularized subspace methods. We leverage these properties to develop an adaptive sliding-window controller for linear time-varying (LTV) systems. To guarantee safety despite closed-loop data correlations, we derive a uniform-in-time, finite-sample confidence bound on the empirical predictor using vector-valued martingale concentration inequalities. Embedding this statistical uncertainty radius into a dynamically tightened constraint set rigorously ensures robust recursive feasibility and Input-to-State practical Stability (ISpS) with high probability. Simulations on LTI and LTV benchmarks demonstrate real-time tractability and strict constraint satisfaction.
Real-time control of multivariable nonlinear processes requires models balancing high fidelity with computational tractability. This paper compares two data-driven paradigms: Bilinear Koopman Realizations and Physics-Informed Neural Networks. While standard Koopman approaches seek global linearization, we leverage a bilinear framework in the lifted functional space to preserve the natural coupling of control-affine systems. Simultaneously, PINNs ensure physical consistency by embedding conservation laws into the learning objective. To facilitate high-performance control, both surrogate models are integrated into a nonlinear model predictive control scheme using the CasADi framework, enabling efficient algorithmic differentiation for optimization. Simulation results for a quadruple tank system demonstrate that both paradigms reach mean VAF values above 99%, but the Bilinear Koopman model delivers a lower mean RMSE during step transients while doubling the computational speed of the PINN with a Real-Time Factor above 22. We conclude that despite structural scaling limitations regarding neural exploding gradients and operator instability risks, the Bilinear Koopman realization provides a more reliable, noise-resilient solution for real-time hydraulic benchmarks.
Amir Vanegas, Julio Barón-Velandia, Nelson Leonardo Díaz-Aldana et al.· International Conference on...· 0 citations