TY - JOUR
N2 - 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.
L1 - http://sp.czasopisma.pan.pl/Content/111268/PDF/04_art_ACS-2019-1_INTERNET.pdf
L2 - http://sp.czasopisma.pan.pl/Content/111268
PY - 2019
IS - No 1
EP - 57-71
KW - lack of controllability
KW - exact controllability
KW - approximate controllability
KW - null controllability
KW - Green’s function
KW - heuristic method
KW - infinite system of algebraic equations
KW - regularity
KW - fully regularity
A1 - Khurshudyan, Asatur Zh.
PB - Committee of Automatic Control and Robotics PAS
VL - vol. 29
DA - 2019.03.28
T1 - Distributed controllability of one-dimensional heat equation in unbounded domains: The Green’s function approach
SP - 57-71
UR - http://sp.czasopisma.pan.pl/dlibra/publication/edition/111268
DOI - 10.24425/acs.2019.127523
ER -