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.

JO - Archives of Control Sciences L1 - http://www.czasopisma.pan.pl/Content/114623/PDF/ACS-2019-4-1.pdf L2 - http://www.czasopisma.pan.pl/Content/114623 IS - No 4 EP - 584 KW - lack of controllability KW - constrained controllability KW - heuristic method KW - averaged dynamics KW - uniformly distributed random variable ER - A1 - Klamka, Jerzy A1 - Khurshudyan, Asatur Zh. PB - Committee of Automatic Control and Robotics PAS VL - vol. 29 JF - Archives of Control Sciences SP - 573 T1 - Averaged controllability of heat equation in unbounded domains with random geometry and location of controls: The Greenâ€™s function approach UR - http://www.czasopisma.pan.pl/dlibra/docmetadata?id=114623 DOI - 10.24425/acs.2019.131226