Exact gradient controllability with strategic actuators

Resumo

In this paper, we develop results related to the gradient controllability and actuators. The concept of gradient strategic actuators is characterized and applied to the gradient controllability of systems described by a hyperbolic equation. This emphasizes the spatial structure and the location of the actuator in order to achieve the gradient controllability. We combine the Hilbert uniqueness method and the characterization of the strategic actuators to solve the gradient controllability problem for the wave equation. The developed results are illustrated by many examples of specific shapes and systems.