Submodularity of Energy Related Controllability Metrics

Abstract

The quantification of controllability and observability has recently received new interest in the context of large, complex networks of dynamical systems. A fundamental but computationally difficult problem is the placement or selection of actuators and sensors that optimize real-valued controllability and observability metrics of the network. We show that several classes of energy related metrics associated with the controllability Gramian in linear dynamical systems have a strong structural property, called submodularity. This property allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and for placement of power electronic actuators in a model of the European power grid.

7 pages, 2 figures; submitted to the 2014 IEEE Conference on Decision and Control

Cited by in corpus (5)

• Control Principles of Complex Networks
• On Submodularity and Controllability in Complex Dynamical Networks
• On the Role of Network Centrality in the Controllability of Complex Networks
• Actuator Security Indices Based on Perfect Undetectability: Computation, Robustness, and Sensor Placement
• The Observability Radius of Networks