Distributed controllability of one-dimensional heat equation in unbounded domains: The Green's function approach

• Autorzy: Khurshudyan Asatur Zh.

Identyfikatory

DOI

10.24425/acs.2019.127523

• Języki publikacji: EN

Abstrakty

EN

We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L²-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.

Słowa kluczowe

EN

lack of controllability; exact controllability; approximate controllability; nullcontrollability; Green’s function; heuristic method; infinite system of algebraic equations; regularity; fully regularity

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 1
• Strony: 57--71
• Opis fizyczny: Bibliogr. 25 poz., wzory

Twórcy

autor

Khurshudyan Asatur Zh.

• Department on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, 24B Baghramyan Ave., 0019 Yerevan, Armenia
• Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, P. R. China

Bibliografia

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Uwagi

EN

1. To the 80th birthday of my father Zhora Khurshudyan, a talented engineer and inventor, is dedicated. I acknowledge the funding of my postdoctoral research at the Institute of Natural Sciences, Shanghai Jiao Tong University from the State Administration of Foreign Experts Affairs of China. I am also thankful to Prof. Min Tang for her invaluable contribution into my personal career development.

PL

2. Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).