Does the boundary controlled heat equation define an exactly controllable system?

Abstract: It is commonly accepted in the control theory of PDEs that parabolic equations, due to the smoothing effect, do not determine exactly controllable systems when controlled from the boundary. The aim of this presentation is to explain how the heat semigroup can be restricted to an appropriate function space on which, when controlled from the boundary, it could determine an exactly controllable systems. To this aim, we first recall some abstract concepts concerning reachability in an infinite dimensional context, insisting on the general relevance of the concept of reachable space. We next describe some recent advances on the reachable space of the boundary controlled heat equation in one space dimension. We next discuss the exact controllability of this system in appropriate spaces of analytic functions. We give applications in determining the reachable space with smooth inputs, with possible application to nonlinear problems. Finally, we discuss the possible implications of our methods to improve the existing estimates of the control constant in small time.

analysis of PDEsoptimization and control

Audience: learners

Control in Times of Crisis. Online seminar.

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