Kernels for linear time invariant system identification

TL;DR

This paper introduces kernel-based methods for identifying the impulse response of LTI systems from noisy data, emphasizing the design of kernels that encode system properties for improved modeling.

Contribution

It develops a framework for constructing and characterizing kernels tailored for LTI system identification, incorporating properties like stability and smoothness, and explores kernel learning for automatic model selection.

Findings

Designed kernels that encode system stability and smoothness.

Demonstrated the effectiveness of kernel learning in system identification.

Provided a systematic approach for temporal impulse response modeling.

Abstract

In this paper, we study the problem of identifying the impulse response of a linear time invariant (LTI) dynamical system from the knowledge of the input signal and a finite set of noisy output observations. We adopt an approach based on regularization in a Reproducing Kernel Hilbert Space (RKHS) that takes into account both continuous and discrete time systems. The focus of the paper is on designing spaces that are well suited for temporal impulse response modeling. To this end, we construct and characterize general families of kernels that incorporate system properties such as stability, relative degree, absence of oscillatory behavior, smoothness, or delay. In addition, we discuss the possibility of automatically searching over these classes by means of kernel learning techniques, so as to capture different modes of the system to be identified.