Actuator placement in networks using optimal control performance metrics
Tyler Holt Summers · 2016
Quantifying controllability in large dynamical networks and designing network structures with good controllability properties has generated significant recent interest. We consider actuator placement problems in dynamical networks and show that the mappings from actuator subsets to four fundamental optimal control metrics are in general neither supermodular nor submodular set functions via a simple counterexample. We also find a set of restrictive conditions under which these mappings are modular set functions. Although this implies that simple greedy algorithms do not in general produce actuator placements with guaranteed near optimal closed-loop control performance, we find in computational experiments that greedy algorithms can exceed performance and far exceed scalability of convex relaxation heuristics with general purpose semidefinite programming solvers.