Optimal actuator/sensor placement for linear parabolic PDEs using spatial H₂ norm

The present work focuses on the optimal, with respect to certain criteria, placement of control actuators and sensors for transport-reaction processes which are mathematically modeled by linear parabolic partial differential equations. Using modal decomposition to discretize the spatial coordinate, and the notions of spatial and modal controllability and observability, the semi-infinite optimization problem is formulated as a nonlinear optimization problem in an abstract space, which is subsequently solved using standard search algorithms. The proposed method is successfully applied to a representative process, modeled by a one-dimensional parabolic PDE, where the optimal location of a single and multiple point actuators are computed.