Bang-Bang Property of Time Optimal Control for a Kind of Microwave Heating Problem

Dongsheng Luo (), Wei Wei (), Yumei Liao () and Hongyong Deng ()
Additional contact information
Dongsheng Luo: Guizhou University
Wei Wei: Guizhou University
Yumei Liao: Guizhou University
Hongyong Deng: Guizhou Minzu University

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 1, No 16, 317-331

Abstract: Abstract In this paper, the bang–bang property and the existence of the solution for the time optimal control of a specific kind of microwave heating problem are studied. The mathematical model for the time optimal control problem (P) of microwave heating is formulated, in which the governing equations of the controlled system are the weak coupling system of Maxwell equations and the heat equation. Based on a new observability estimate of the heat controlled system, the controllability of the system is derived by proving the null controllability of an equivalent system. The existence of the time optimal control of microwave heating is acquired under some stated assumptions, enabling the bang–bang property of the time optimal control problem (P) to be achieved.

Keywords: Time optimal control; Bang–bang property; Carleman inequality; Microwave heating; Null controllability; Observability estimate; 49K15; 49K30; 35B35 (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-019-01559-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:183:y:2019:i:1:d:10.1007_s10957-019-01559-y

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-019-01559-y

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().