Optimal Sensor and Actuator Placement in Complex Dynamical Networks

摘要

Controllability and observability have long been recognized as fundamentalstructural properties of dynamical systems, but have recently seen renewedinterest in the context of large, complex networks of dynamical systems. Abasic problem is sensor and actuator placement: choose a subset from a finiteset of possible placements to optimize some real-valued controllability andobservability metrics of the network. Surprisingly little is known about thestructure of such combinatorial optimization problems. In this paper, we showthat an important class of metrics based on the controllability andobservability Gramians has a strong structural property that allows efficientglobal optimization: the mapping from possible placements to the trace of theassociated Gramian is a modular set function. We illustrate the results viaplacement of power electronic actuators in a model of the European power grid.