Stable Linear System Identification with Prior Knowledge by Riemannian Sequential Quadratic Optimization

TL;DR

This paper introduces a novel Riemannian optimization approach for stable linear system identification from noisy data, ensuring stability and prior knowledge constraints with theoretical guarantees and improved effectiveness.

Contribution

It formulates the system identification as a Riemannian nonlinear optimization problem and applies RSQO to solve it more efficiently than existing methods.

Findings

RSQO effectively solves the stability-constrained identification problem.

The proposed method outperforms competing algorithms in accuracy and efficiency.

The approach guarantees convergence to KKT points with theoretical support.

Abstract

We consider an identification method for a linear continuous time-invariant autonomous system from noisy state observations. In particular, we focus on the identification to satisfy the asymptotic stability of the system with some prior knowledge. To this end, we propose to model this identification problem as a Riemannian nonlinear optimization (RNLO) problem, where the stability is ensured through a certain Riemannian manifold and the prior knowledge is expressed as nonlinear constraints defined on this manifold. To solve this RNLO, we apply the Riemannian sequential quadratic optimization (RSQO) that was proposed by Obara, Okuno, and Takeda (2022) most recently. RSQO performs quite well with theoretical guarantee to find a point satisfying the Karush-Kuhn-Tucker conditions of RNLO. In this paper, we demonstrate that the identification problem can be indeed solved by RSQO more effectively than competing algorithms.