Kernel-based models for system analysis

2021/10/22 by Henk J. van Waarde, Rodolphe Sepulchre, van Waarde, Henk J. +1 · 4 citations
Engineering · Physics and Astronomy · #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Mathematics #Fault Detection and Control Systems #Model Reduction and Neural Networks #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2110.11735

openalex publication_date 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized by suitable input-output properties required for system analysis and control design. This biased identification problem is shown to admit the tractable solution of a regularized least squares problem when formulated in a suitable reproducing kernel Hilbert space. The kernel-based framework is a departure from the prevailing state-space framework. It is motivated by fundamental limitations of nonlinear state-space models at combining the fitting requirements of data-based modeling with the input-output requirements of system analysis and physical modeling.

Cited by

• Identification of contractive Lur'e-type systems via kernel-based Lipschitz design
• Data-driven control of network systems: Accounting for communication adaptivity and security
• Stabilization of Nonlinear Systems with State-Dependent Representation: From Model-Based to Direct Data-Driven Control
• Passive nonlinear FIR filters for data-driven control

Related

• A kernel-based approach to physics-informed nonlinear system identification
• The Existence and Uniqueness of Solutions for Kernel-Based System Identification
• Kernel Methods for the Approximation of Nonlinear Systems
• Kernels for linear time invariant system identification
• On kernel design for regularized LTI system identification