TY - JOUR
N2 - 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.
L1 - http://so.czasopisma.pan.pl/Content/114623/PDF/ACS-2019-4-1.pdf
L2 - http://so.czasopisma.pan.pl/Content/114623
PY - 2019
IS - No 4
EP - 584
DO - 10.24425/acs.2019.131226
KW - lack of controllability
KW - constrained controllability
KW - heuristic method
KW - averaged dynamics
KW - uniformly distributed random variable
A1 - Klamka, Jerzy
A1 - Khurshudyan, Asatur Zh.
PB - Committee of Automatic Control and Robotics PAS
VL - vol. 29
DA - 2019.11.28
T1 - Averaged controllability of heat equation in unbounded domains with random geometry and location of controls: The Green’s function approach
SP - 573
UR - http://so.czasopisma.pan.pl/dlibra/publication/edition/114623
T2 - Archives of Control Sciences
ER -