77 research outputs found
Signal selection for estimation and identification in networks of dynamic systems: a graphical model approach
Network systems have become a ubiquitous modeling tool in many areas of
science where nodes in a graph represent distributed processes and edges
between nodes represent a form of dynamic coupling. When a network topology is
already known (or partially known), two associated goals are (i) to derive
estimators for nodes of the network which cannot be directly observed or are
impractical to measure; and (ii) to quantitatively identify the dynamic
relations between nodes. In this article we address both problems in the
challenging scenario where only some outputs of the network are being measured
and the inputs are not accessible. The approach makes use of the notion of
-separation for the graph associated with the network. In the considered
class of networks, it is shown that the proposed technique can determine or
guide the choice of optimal sparse estimators. The article also derives
identification methods that are applicable to cases where loops are present
providing a different perspective on the problem of closed-loop identification.
The notion of -separation is a central concept in the area of probabilistic
graphical models, thus an additional contribution is to create connections
between control theory and machine learning techniques.Comment: Under review for publication on IEEE Transaction on Automatic Contro
Realizing Information Erasure in Finite Time
In this article, we focus on erasure of a bit of information in finite time.
Landauer's principle states that the average heat dissipation due to erasure of
information is k_B T ln 2, which is achievable only in an asymptotic manner.
Recent theoretical developments in non-equilibrium thermodynamics and
stochastic control, predict a more general bound for finite time erasure
dependent on the Wasserstein distances between the initial and final
configurations. These predictions suggest improvements to experimental protocol
with regards to minimizing average heat dissipation for bit erasure in finite
time from a bistable well, under overdamped Langevin dynamics. We present a
comparative study of a theoretically optimal protocol with an existing
protocol, and highlight the closeness and deviation from optimalityComment: Conference on Decisions and Controls 201
A Stochastic Markov Model for Coordinated Molecular Motors
Many cell functions are accomplished thanks to intracellular transport
mechanisms of macromolecules along filaments. Molecular motors such as dynein
or kinesin are proteins playing a primary role in these processes. The behavior
of such proteins is quite well understood when there is only one of them moving
a cargo particle. Indeed, numerous in vitro experiments have been performed to
derive accurate models for a single molecular motor. However, in vivo
macromolecules are often carried by multiple motors. The main focus of this
paper is to provide an analysis of the behavior of more molecular motors
interacting together in order to improve the understanding of their actual
physiological behavior. Previous studies provide analyses based on results
obtained from Monte Carlo simulations. Different from these studies, we derive
an equipollent probabilistic model to describe the dynamics of multiple
proteins coupled together and provide an exact theoretical analysis. We are
capable of obtaining the probability density function of the motor protein
configurations, thus enabling a deeper understanding of their behavior
Hysteresis Models of Dynamic Mode Atomic Force Microscopes: Analysis and Identification
A new class of models based on hysteresis functions is developed to describe
atomic force microscopes operating in dynamic mode. Such models are able to
account for dissipative phenomena in the tip-sample interaction which are
peculiar of this operation mode. The model analysis, which can be pursued using
frequency domain techniques, provides a clear insight of specific nonlinear
behaviours. Experiments show good agreement with the identified models.Comment: 19 pages, 7 figure
Data-driven identification of a thermal network in multi-zone building
System identification of smart buildings is necessary for their optimal
control and application in demand response. The thermal response of a building
around an operating point can be modeled using a network of interconnected
resistors with capacitors at each node/zone called RC network. The development
of the RC network involves two phases: obtaining the network topology, and
estimating thermal resistances and capacitance's. In this article, we present a
provable method to reconstruct the interaction topology of thermal zones of a
building solely from temperature measurements. We demonstrate that our learning
algorithm accurately reconstructs the interaction topology for a zone
office building in EnergyPlus with real-world conditions. We show that our
learning algorithm is able to recover the network structure in scenarios where
prior research prove insufficient.Comment: 6 pages, 12 figures, 57th IEEE Conference on Decision and Contro
Error Bounds on a Mixed Entropy Inequality
Motivated by the entropy computations relevant to the evaluation of decrease
in entropy in bit reset operations, the authors investigate the deficit in an
entropic inequality involving two independent random variables, one continuous
and the other discrete. In the case where the continuous random variable is
Gaussian, we derive strong quantitative bounds on the deficit in the
inequality. More explicitly it is shown that the decay of the deficit is
sub-Gaussian with respect to the reciprocal of the standard deviation of the
Gaussian variable. What is more, up to rational terms these results are shown
to be sharp
Topology Learning of Radial Dynamical Systems with Latent Nodes
In this article, we present a method to reconstruct the topology of a
partially observed radial network of linear dynamical systems with
bi-directional interactions. Our approach exploits the structure of the inverse
power spectral density matrix and recovers edges involving nodes up to four
hops away in the underlying topology. We then present an algorithm with
provable guarantees, which eliminates the spurious links obtained and also
identifies the location of the unobserved nodes in the inferred topology. The
algorithm recovers the exact topology of the network by using only time-series
of the states at the observed nodes. The effectiveness of the method developed
is demonstrated by applying it on a typical distribution system of the electric
grid.Comment: 6 page
Topology Estimation in Bulk Power Grids: Guarantees on Exact Recovery
The topology of a power grid affects its dynamic operation and settlement in
the electricity market. Real-time topology identification can enable faster
control action following an emergency scenario like failure of a line. This
article discusses a graphical model framework for topology estimation in bulk
power grids (both loopy transmission and radial distribution) using
measurements of voltage collected from the grid nodes. The graphical model for
the probability distribution of nodal voltages in linear power flow models is
shown to include additional edges along with the operational edges in the true
grid. Our proposed estimation algorithms first learn the graphical model and
subsequently extract the operational edges using either thresholding or a
neighborhood counting scheme. For grid topologies containing no three-node
cycles (two buses do not share a common neighbor), we prove that an exact
extraction of the operational topology is theoretically guaranteed. This
includes a majority of distribution grids that have radial topologies. For
grids that include cycles of length three, we provide sufficient conditions
that ensure existence of algorithms for exact reconstruction. In particular,
for grids with constant impedance per unit length and uniform injection
covariances, this observation leads to conditions on geographical placement of
the buses. The performance of algorithms is demonstrated in test case
simulations.Comment: 10 pages, 8 figures. A version of this paper will appear in IREP 201
Exact Topology Learning in a Network of Cyclostationary Processes
Learning the structure of a network from time series data, in particular
cyclostationary data, is of significant interest in many disciplines such as
power grids, biology and finance. In this article, an algorithm is presented
for reconstruction of the topology of a network of cyclostationary processes.
To the best of our knowledge, this is the first work to guarantee exact
recovery without any assumptions on the underlying structure. The method is
based on a lifting technique by which cyclostationary processes are mapped to
vector wide sense stationary processes and further on semi-definite properties
of matrix Wiener filters for the said processes.We demonstrate the performance
of the proposed algorithm on a Resistor-Capacitor network and present the
accuracy of reconstruction for varying sample sizes.Comment: 6 pages, 3 figures, A version of this paper will appear in American
Control Conference 201
Graphical Models in Meshed Distribution Grids: Topology estimation, change detection and limitations
Graphical models are a succinct way to represent the structure in probability
distributions. This article analyzes the graphical model of nodal voltages in
non-radial power distribution grids. Using algebraic and structural properties
of graphical models, algorithms exactly determining topology and detecting line
changes for distribution grids are presented along with their theoretical
limitations. We show that if distribution grids have cycles/loops of size
greater than three, then nodal voltages are sufficient for efficient topology
estimation without additional assumptions on system parameters. In contrast,
line failure or change detection using nodal voltages does not require any
structural assumption. Under noisy measurements, we provide the first
non-trivial bounds on the maximum noise that the system can tolerate for
asymptotically correct topology recovery. The performance of the designed
algorithms is validated with nonlinear AC power flow samples generated by
Matpower on test grids, including scenarios with injection correlations and
system noise.Comment: 12 pages, 9 figures, IEEE Transactions on Smart Gri
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