Data-driven methods for L2-gain estimation
2009 (English)In: IFAC Proceedings Volumes (IFAC-PapersOnline), Saint-Malo, 2009, Vol. 15, no PART 1, 1597-1602 p.Conference paper (Refereed)
In this paper we present and discuss some data-driven methods for estimation of the L2-gain of dynamical systems. Partial results on convergence and statistical properties are provided. The methods are based on multiple experiments on the system. The main idea is to directly estimate the maximizing input signal by using iterative experiments on the true system. We study such a data-driven method based on a stochastic gradient method. We show that this method is very closely related to the so-called power iteration method based on the power method in numerical analysis. Furthermore, it is shown that this method is applicable for linear systems with noisy measurements. We will also study L2-gain estimation of Hammerstein systems. The stochastic gradient method and the power iteration method are evaluated and compared in simulation examples. Â© 2009 IFAC.
Place, publisher, year, edition, pages
Saint-Malo, 2009. Vol. 15, no PART 1, 1597-1602 p.
, 15th IFAC Symposium on System Identification, SYSID 2009
Infinity norm, Input signal design, L2-gain estimation, Power method, Small gain theorem, Gain estimation, Dynamical systems, Estimation, Experiments, Gradient methods, Linear systems, Numerical analysis, Stochastic systems, Numerical methods
IdentifiersURN: urn:nbn:se:kth:diva-55391DOI: 10.3182/20090706-3-FR-2004.0253ScopusID: 2-s2.0-80051613040OAI: oai:DiVA.org:kth-55391DiVA: diva2:471643
Sponsors: IFAC Tech. Comm. Model., Identif. Signal Process.; IFAC Technical Committee on Adaptive and Learning Systems; IFAC Technical Committee on Discrete Events and Hybrid Systems; IFAC Technical Committee on Stochastic Systems; IEEE Control Systems Society2012-01-272012-01-022013-09-05Bibliographically approved