Gray Box Identification of State-Space Models Using Difference of Convex Programming

TL;DR

This paper introduces a novel gray-box system identification method leveraging difference-of-convex programming and low-rank Hankel matrices, improving initial estimates and robustness in structured state-space modeling.

Contribution

It recasts gray-box identification as a difference-of-convex problem solved via sequential convex programming with nuclear-norm initialization, overcoming previous non-convexity issues.

Findings

Achieves maximum impulse-response fitting without non-convex conditions.

Applicable even when system parameters are unidentifiable.

Provides reliable initial estimates for iterative refinement.

Abstract

Gray-box identification is prevalent in modeling physical and networked systems. However, due to the non-convex nature of the gray-box identification problem, good initial parameter estimates are crucial for a successful application. In this paper, a new identification method is proposed by exploiting the low-rank and structured Hankel matrix of impulse response. This identification problem is recasted into a difference-of-convex programming problem, which is then solved by the sequential convex programming approach with the associated initialization obtained by nuclear-norm optimization. The presented method aims to achieve the maximum impulse-response fitting while not requiring additional (non-convex) conditions to secure non-singularity of the similarity transformation relating the given state-space matrices to the gray-box parameterized ones. This overcomes a persistent shortcoming in a number of recent contributions on this topic, and the new method can be applied for the structured state-space realization even if the involved system parameters are unidentifiable. The method can be used both for directly estimating the gray-box parameters and for providing initial parameter estimates for further iterative search in a conventional gray-box identification setup.