Robustness of the controllability for the heat equation under the influence of multiple impulses and delays

Abstract

For many control systems in real life, impulses and delays are intrinsic properties that do not modify their behavior. Thus, we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system, that could model a real situation, do not modify properties such as controllability. In this regard, we prove the approximate controllability of the semilinear heat equation under the influence of multiple impulses and delays, this is done by using new techniques, avoiding fixed point theorems, employed by A.E. Bashirov et al.

Mathematics Subject Classification (2010): Primary: 93B05; Secondary: 93C10.

Keywords: Robustness, interior approximate controllability, semilinear heat equation with impulses and delays, strongly continuous semigroup