We address the problem of minimal cost actuator/ sensor placement for large scale linear time invariant (LTI) systems that ensures structural controllability/observability. In particular, for the dedicated actuator placement problem (i.e., each actuator can control only one state variable or dynamic component), we propose a design methodology that provides the optimal placement with minimal cost (with respect to a given placement cost functional), under the requirement that the system be structurally controllable. In addition of obtaining the global solution of the optimization problem, the methodology is shown to be implemented by an algorithm with polynomial complexity (in the number of state variables), making it suitable for large scale systems. By duality, the solution readily extends to the structural design of the corresponding sensor placement under cost constraints.
