LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation

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Abstract

A model of boundary control system with boundary observation is described and analyzed, which involves no unbounded operator except for the dynamics generator. The resolution of a LQ-optimal control problem for this model provides a stabilizing feedback for a nominal system with unbounded operators. The model consists of an extended abstract differential equation whose state components are the boundary input, the state (up to an affine transformation) and a Yosida-type approximation of the output of the nominal system. It is shown that, under suitable conditions, the model is well-posed and, in particular, that the dynamics operator is the generator of an analytic C0- semigroup and the model is observable. A LQ-optimal control problem is posed for the model, and a general method of resolution based on the problem of spectral factorization of a multi-dimensional operator-valued spectral density is described. It is expected that this approach will lead hopefully to a good trade-off between the cost of modelling and the efficiency of methods of resolution of control problems for such systems.

Original languageEnglish
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1071-1076
Number of pages6
ISBN (Print)9781467357173
DOIs
Publication statusPublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: 10 Dec 201313 Dec 2013

Conference

Conference52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period10/12/1313/12/13

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  • Cite this

    Dehaye, J. R., & Winkin, J. J. (2013). LQ-optimal control by spectral factorization of extended semigroup boundary control systems with approximate boundary observation. In Proceedings of the IEEE Conference on Decision and Control (pp. 1071-1076). [6760024] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760024