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dc.contributor.authorRen, Z.
dc.contributor.authorXu, C.
dc.contributor.authorLin, Qun
dc.contributor.authorLoxton, Ryan
dc.contributor.editorAlessandro Astolfi
dc.date.accessioned2017-01-30T11:50:52Z
dc.date.available2017-01-30T11:50:52Z
dc.date.created2015-08-04T20:00:51Z
dc.date.issued2015
dc.identifier.citationRen, Z. and Xu, C. and Lin, Q. and Loxton, R. 2015. Output stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization, in Proceedings of the 2015 American Control Conference, Jul 1-3 2015, pp. 4257-4262. Chicago: IEEE.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/15628
dc.identifier.doi10.1109/ACC.2015.7171998
dc.description.abstract

This paper proposes a new control synthesis approach for the stabilization of boundary-controlled parabolic partial differential equations (PDEs). In the proposed approach, the optimal boundary control is expressed in integral state feedback form with quadratic kernel function, where the quadratic’s coefficients are decision variables to be optimized. We introduce a system cost functional to penalize both state and kernel magnitude, and then derive the cost functional’s gradient in terms of the solution of an auxiliary “costate” PDE. On this basis, the output stabilization problem can be solved using gradient-based optimization techniques such as sequential quadratic programming. The resulting optimal boundary control is guaranteed to yield closed-loop stability under mild conditions. The primary advantage of our new approach is that the costate PDE is in standard form and can be solved easily using the finite difference method. In contrast, the traditional control synthesis approaches for boundary-controlled parabolic PDEs (i.e., the LQ control and backstepping approaches) require solving non-standard Riccati-type and Klein-Gorden-type PDEs.

dc.publisherIEEE
dc.titleOutput stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization
dc.typeConference Paper
dcterms.source.startPage4257
dcterms.source.endPage4262
dcterms.source.titleProceedings of the 2015 American Control Conference
dcterms.source.seriesProceedings of the 2015 American Control Conference
dcterms.source.isbn9781479986866
dcterms.source.conference2015 American Control Conference
dcterms.source.conference-start-dateJul 1 2015
dcterms.source.conferencelocationChicago, USA
dcterms.source.placeChicago, USA
curtin.note

Copyright © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

curtin.departmentDepartment of Mathematics and Statistics
curtin.accessStatusOpen access


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