CONSTRAINED APPROXIMATE NULL CONTROLLABILITY OF THE COUPLED HEAT EQUATION WITH IMPULSE CONTROLS.

This paper is concerned with the constrained approximate null controllability of the heat equation coupled with a real matrix P, where the controls are impulsive and periodically act into the system through a series of real matrices \{ Qk\} ~ k=1. The conclusions are given in two cases. In the case that the controls act globally into the system, we prove that the system is global constrained approximate null controllable under a spectral condition of P together with a rank condition of P and \{ Qk\} ~ k=1, while in the case that the controls act locally into the system, we prove the global constrained approximate null controllability under a stronger condition for P and the same rank condition as the above case. Moreover, we prove that the above-mentioned spectral condition of P is necessary for global constrained approximate null controllability of the control problem considered in this paper. [ABSTRACT FROM AUTHOR]