Finite time identification in unstable linear systems. (October 2018)

• Record Type: Journal Article
• Authors: Shirani Faradonbeh, Mohamad Kazem; Tewari, Ambuj; Michailidis, George
• Is Part Of: Automatica. Volume 96(2018)
• Page Start: 342
• Page End: 353
• Publication Date: 2018-10
• Subjects: Linear dynamics -- Finite time stabilization -- Stochastic control -- Adaptive control -- Autoregressive process -- Non-asymptotic estimation; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2018.07.008
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensionalsettings. However, there are hardly any results for the unstable case, especially regarding finite time bounds . For this setting, classical results on least-squares estimation of the dynamics parameters are not applicable and therefore new concepts and technical approaches need to be developed to address the issue. Unstable linear systems arise in key real applications in control theory, econometrics, and finance. This study establishes finite time bounds for the identification error of the least-squares estimates for a fairly large class of heavy-tailed noise distributions, and transition matrices of such systems. The results relate the time length (samples) required for estimation to a function of the problem dimension and key characteristics of the true underlying transition matrix and the noise distribution. To establish them, appropriate concentration inequalities for random matrices and for sequences of martingale differences are leveraged.