Switching Controls for Analytic Semigroups and Applications to Parabolic Systems

In this work, we extend the analysis of problem switching controls proposed in [E. Zuazua, J. Eur. Math. Soc. (JEMS), 13 (2011), pp. 85--117]. The asks following question: Assuming that one can control a system using two or more actuators, does there exist strategy such at all times, only actuator is active? We answer positively when controlled corresponds to an analytic semigroup spanned by positive self-adjoint operator which null-controllable arbitrary small times. Similarly 85--117], our proof relies on analyticity arguments and will also work finite dimensional settings under some further spectral assumptions spans but not necessarily self-adjoint.