Actuator Placement Under Structural Controllability Using Forward and Reverse Greedy Algorithms

Actuator placement is an active field of research, which has received significant attention for its applications in complex dynamical networks. In this article, we study the problem finding a set actuator placements minimizing metric that measures average energy consumed state transfer by controller, while satisfying structural controllability requirement and cardinality constraint on number actuators allowed. As no computationally efficient methods are known to solve such combinatorial function optimization problems, two greedy algorithms, forward reverse, proposed obtain approximate solutions. We first show sets these algorithms explore can be characterized matroids. then performance guarantees reverse applied general class matroid problems exploiting properties objective as submodularity ratio curvature. Finally, propose feasibility check both based maximum flow certain auxiliary graphs originating from network graph. Our results verified with case studies over large