CONTROLLABILITY PROBLEMS FOR THE HEAT EQUATION ON A HALF-AXIS WITH A BOUNDED CONTROL IN THE NEUMANN BOUNDARY CONDITION

摘要

In the paper, the problems of controllability and approximate controllability are studied for the control system w(t) = w(xx), w(x) (0, .) = u, x > 0, t is an element of (0, T), where u is an element of L-infinity(0, T) is a control. It is proved that each initial state of the system is approximately controllable to each target state in a given time T. A necessary and sufficient condition for controllability in a given time T is obtained in terms of solvability of a Markov power moment problem. It is also shown that there is no initial state which is null-controllable in a given time T. Orthogonal bases are constructed in H-1 and H-1. Using these bases, numerical solutions to the approximate controllability problem are obtained. The results are illustrated by examples.