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.

JO - Archives of Control Sciences L1 - http://www.czasopisma.pan.pl/Content/111268/PDF/04_art_ACS-2019-1_INTERNET.pdf L2 - http://www.czasopisma.pan.pl/Content/111268 IS - No 1 EP - 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 ER - A1 - Khurshudyan, Asatur Zh. PB - Committee of Automatic Control and Robotics PAS VL - vol. 29 JF - Archives of Control Sciences SP - 57 T1 - Distributed controllability of one-dimensional heat equation in unbounded domains: The Green’s function approach UR - http://www.czasopisma.pan.pl/dlibra/docmetadata?id=111268 DOI - 10.24425/acs.2019.127523