Title :
Submodularity of energy related controllability metrics
Author :
Cortesi, Fabrizio L. ; Summers, Tyler H. ; Lygeros, John
Author_Institution :
ETH Zurich, Zurich, Switzerland
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, which allows for an approximation guarantee by using a simple greedy heuristic for their maximization. The results are illustrated for randomly generated systems and placement of power electronic actuators in a model of the European power grid.
Keywords :
actuators; complex networks; controllability; greedy algorithms; large-scale systems; linear systems; optimisation; sensor placement; European power grid; actuator placement; actuator selection; complex network; controllability Gramian; energy related controllability metrics; greedy heuristic; large network; linear dynamical systems; maximization; observability; power electronic actuators; sensor placement; sensor selection; structural property; submodularity; Actuators; Aerospace electronics; Controllability; Eigenvalues and eigenfunctions; Measurement; Symmetric matrices; Tin;
Conference_Titel :
Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on
Conference_Location :
Los Angeles, CA
Print_ISBN :
978-1-4799-7746-8
DOI :
10.1109/CDC.2014.7039832