Averaged controllability of heat equation in unbounded domains with random geometry and location of controls: The Green’s function approach

• Autorzy: Klamka Jerzy , Khurshudyan Asatur Zh.

Identyfikatory

DOI

10.24425/acs.2019.131226

• Języki publikacji: EN

Abstrakty

EN

The constrained averaged controllability of linear one-dimensional heat equation defined on R and R₊ is studied. The control is carried out by means of the time-dependent intensity of a heat source located at an uncertain interval of the corresponding domain, the end-points of which are considered as uniformly distributed random variables. Employing the Green’s function approach, it is shown that the heat equation is not constrained averaged controllable neither in R nor in R⁺. Sufficient conditions on initial and terminal data for the averaged exact and approximate controllabilities are obtained. However, constrained averaged controllability of the heat equation is established in the case of point heat source, the location of which is considered as a uniformly distributed random variable. Moreover, it is obtained that the lack of averaged controllability occurs for random variables with arbitrary symmetric density function.

Słowa kluczowe

EN

lack of controllability; constrained controllability; heuristic method; averaged dynamics; uniformly distributed random variable

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 4
• Strony: 573--584
• Opis fizyczny: Bibliogr. 19 poz., wzory

Twórcy

autor

Klamka Jerzy

• Institute of Control Engineering, Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Gliwice, Poland

autor

Khurshudyan Asatur Zh.

• Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai,China
• andDepartment onDynamics ofDeformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia

Bibliografia

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• [3] S. Micu and E. Zuazua: On the lack of null controllability of the heat equation on the half space. Portugaliae Mathematica, 58 (2001), 1-24.
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• [16] J. Klamka: Controllability and Minimum Energy Control. Springer, Cham, 2019.
• [17] As. Zh. Khurshudyan: Heuristic determination of resolving controls for exact and approximate controllability of nonlinear dynamic systems. Mathematical Problems in Engineering, article ID 9496371, 16 pages (2018).
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• [19] As. Zh. Khurshudyan: Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach. Archives of Control Sciences, 28(3), (2018), 335-347.

Uwagi

PL

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