Identification of Structured LTI MIMO State-Space Models

TL;DR

This paper presents a novel method for identifying structured LTI MIMO state-space models by transforming the problem into a rank-constrained optimization and solving it via difference of convex programming, ensuring global optimality with manageable computation.

Contribution

It introduces a new identification algorithm that converts bilinear estimation into a rank-constrained problem and employs DCP with nuclear norm regularization for high-quality initialization.

Findings

The proposed method effectively finds global solutions.

Numerical examples demonstrate high accuracy.

The approach reduces computational burden compared to existing methods.

Abstract

The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identification method which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial condition for the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initial condition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm.