28,413 research outputs found
On Submodularity and Controllability in Complex Dynamical Networks
Controllability and observability have long been recognized as fundamental
structural properties of dynamical systems, but have recently seen renewed
interest in the context of large, complex networks of dynamical systems. A
basic problem is sensor and actuator placement: choose a subset from a finite
set of possible placements to optimize some real-valued controllability and
observability metrics of the network. Surprisingly little is known about the
structure of such combinatorial optimization problems. In this paper, we show
that several important classes of metrics based on the controllability and
observability Gramians have a strong structural property that allows for either
efficient global optimization or an approximation guarantee by using a simple
greedy heuristic for their maximization. In particular, the mapping from
possible placements to several scalar functions of the associated Gramian is
either a modular or submodular set function. The results are illustrated on
randomly generated systems and on a problem of power electronic actuator
placement in a model of the European power grid.Comment: Original arXiv version of IEEE Transactions on Control of Network
Systems paper (Volume 3, Issue 1), with a addendum (located in the ancillary
documents) that explains an error in a proof of the original paper and
provides a counterexample to the corresponding resul
A Transfer Operator Methodology for Optimal Sensor Placement Accounting for Uncertainty
Sensors in buildings are used for a wide variety of applications such as
monitoring air quality, contaminants, indoor temperature, and relative
humidity. These are used for accessing and ensuring indoor air quality, and
also for ensuring safety in the event of chemical and biological attacks. It
follows that optimal placement of sensors become important to accurately
monitor contaminant levels in the indoor environment. However, contaminant
transport inside the indoor environment is governed by the indoor flow
conditions which are affected by various uncertainties associated with the
building systems including occupancy and boundary fluxes. Therefore, it is
important to account for all associated uncertainties while designing the
sensor layout. The transfer operator based framework provides an effective way
to identify optimal placement of sensors. Previous work has been limited to
sensor placements under deterministic scenarios. In this work we extend the
transfer operator based approach for optimal sensor placement while accounting
for building systems uncertainties. The methodology provides a probabilistic
metric to gauge coverage under uncertain conditions. We illustrate the
capabilities of the framework with examples exhibiting boundary flux
uncertainty
Submodularity of Energy Related Controllability Metrics
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.Comment: 7 pages, 2 figures; submitted to the 2014 IEEE Conference on Decision
and Contro
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