Actuator Placement for Optimizing Network Performance under Controllability Constraints
For control engineers designing large-scale networks, this work offers a theoretically grounded greedy algorithm for actuator placement with performance guarantees.
The paper addresses actuator placement to minimize average control energy while ensuring structural controllability. It provides a greedy algorithm with a novel performance guarantee by reformulating the problem as matroid optimization with a weakly submodular objective.
With the rising importance of large-scale network control, the problem of actuator placement has received increasing attention. Our goal in this paper is to find a set of actuators minimizing the metric that measures the average energy consumption of the control inputs while ensuring structural controllability of the network. As this problem is intractable, greedy algorithm can be used to obtain an approximate solution. To provide a performance guarantee for this approach, we first define the submodularity ratio for the metric under consideration and then reformulate the structural controllability constraint as a matroid constraint. This shows that the problem under study can be characterized by a matroid optimization involving a weakly submodular objective function. Then, we derive a novel performance guarantee for the greedy algorithm applied to this class of optimization problems. Finally, we show that the matroid feasibility check for the greedy algorithm can be cast as a maximum matching problem in a certain auxiliary bipartite graph related to the network graph.