Exact controllability of second-order hyperbolic equations with impulse controls

Abstract

The exact controllability of a class of second-order hyperbolic boundary problems, both linear and semi-linear, with internal impulse controls supported from suitable subdomain is studied. It is shown that if the principal linear part of the hyperbolic equation satisfies Huygens' principle (in a certain sense) and if the aforementioned subdomain is suitably chosen, then such “impulse” exact controllability is possible.

Keywords:

• Second-order hyperbolic equation
• Exact controllability
• Impulse controls
• Huygens’ principle