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On input design for regularized LTI system identification: Power-constrained input
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. Chinese Acad Sci, Peoples R China.
Chinese Univ Hong Kong, Peoples R China.
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 97, p. 327-338Article in journal (Refereed) Published
Abstract [en]

Input design is an important issue for classical system identification methods but has not been investigated for the kernel-based regularization method (KRM) until very recently. In this paper, we consider the input design problem of KRMs for LTI system identification. Different from the recent result, we adopt a Bayesian perspective and in particular make use of scalar measures (e.g., the A-optimality, D-optimality, and E-optimality) of the Bayesian mean square error matrix as the design criteria subject to power-constraint on the input. Instead of solving the optimization problem directly, we propose a two-step procedure. In the first step, by making suitable assumptions on the unknown input, we construct a quadratic map (transformation) of the input such that the transformed input design problems are convex, and the global minima of the transformed input design problem can thus be found efficiently by applying well-developed convex optimization software packages. In the second step, we derive the characterization of the optimal input based on the global minima found in the first step by solving the inverse image of the quadratic map. In addition, we derive analytic results for some special types of kernels, which provide insights on the input design and also its dependence on the kernel structure. (C) 2018 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD , 2018. Vol. 97, p. 327-338
Keywords [en]
Input design; Bayesian mean square error; Kernel-based regularization; LTI system identification; Convex optimization
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-152607DOI: 10.1016/j.automatica.2018.08.010ISI: 000447568400038OAI: oai:DiVA.org:liu-152607DiVA, id: diva2:1262119
Conference
56th IEEE Annual Conference on Decision and Control (CDC)
Note

Funding Agencies|National Natural Science Foundation of China [61773329, 61603379]; Thousand Youth Talents Plan - central government of China; Shenzhen Projects - Shenzhen Science and Technology Innovation Council, China [Ji-20170189, Ji-20160207]; Chinese University of Hong Kong, Shenzhen, China [PF. 01.000249, 2014.0003.23]; Swedish Research Council [20145894]; National Key Basic Research Program of China (973 Program) [2014CB845301]; President Fund of Academy of Mathematics and Systems Science, CAS, China [2015-hwyxqnrc-mbq]

Available from: 2018-11-09 Created: 2018-11-09 Last updated: 2018-11-09

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