Controllability of Coupled Parabolic Systems with Multiple Underactuations

摘要

This work studies the null controllability of an actuated system of coupled parabolic PDEs. In particular, we consider an important subclass of such problems where the couplings are of first and zero-order and the underlying control system is underactuated. We pose our control problem using a recent framework which divides the problem into interconnected parts: we refer to the first part as the analytic control problem, where we use slightly non-classical techniques to prove null controllability by means of internal controls appearing on every equation; we refer to the second part as the algebraic control problem, where we use an algebraic method to “invert” a linear partial differential operator that describes our system; this allows us to recover null controllability by means of internal controls which appear on only a few of the equations. We establish a null controllability result for the original problem by solving these control problems concurrently.