2,019 research outputs found
Minimum Number of Probes for Brain Dynamics Observability
In this paper, we address the problem of placing sensor probes in the brain
such that the system dynamics' are generically observable. The system dynamics
whose states can encode for instance the fire-rating of the neurons or their
ensemble following a neural-topological (structural) approach, and the sensors
are assumed to be dedicated, i.e., can only measure a state at each time. Even
though the mathematical description of brain dynamics is (yet) to be
discovered, we build on its observed fractal characteristics and assume that
the model of the brain activity satisfies fractional-order dynamics.
Although the sensor placement explored in this paper is particularly
considering the observability of brain dynamics, the proposed methodology
applies to any fractional-order linear system. Thus, the main contribution of
this paper is to show how to place the minimum number of dedicated sensors,
i.e., sensors measuring only a state variable, to ensure generic observability
in discrete-time fractional-order systems for a specified finite interval of
time. Finally, an illustrative example of the main results is provided using
electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720
Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes
We aim at studying approximate null-controllability properties of a
particular class of piecewise linear Markov processes (Markovian switch
systems). The criteria are given in terms of algebraic invariance and are
easily computable. We propose several necessary conditions and a sufficient
one. The hierarchy between these conditions is studied via suitable
counterexamples. Equivalence criteria are given in abstract form for general
dynamics and algebraic form for systems with constant coefficients or
continuous switching. The problem is motivated by the study of lysis phenomena
in biological organisms and price prediction on spike-driven commodities.Comment: Mathematics of Control, Signals, and Systems, Springer Verlag
(Germany), 2015, online first
http://link.springer.com/article/10.1007/s00498-015-0146-
Detecting Topology Variations in Dynamical Networks
This paper considers the problem of detecting topology variations in
dynamical networks. We consider a network whose behavior can be represented via
a linear dynamical system. The problem of interest is then that of finding
conditions under which it is possible to detect node or link disconnections
from prior knowledge of the nominal network behavior and on-line measurements.
The considered approach makes use of analysis tools from switching systems
theory. A number of results are presented along with examples
Coverage and Field Estimation on Bounded Domains by Diffusive Swarms
In this paper, we consider stochastic coverage of bounded domains by a
diffusing swarm of robots that take local measurements of an underlying scalar
field. We introduce three control methodologies with diffusion, advection, and
reaction as independent control inputs. We analyze the diffusion-based control
strategy using standard operator semigroup-theoretic arguments. We show that
the diffusion coefficient can be chosen to be dependent only on the robots'
local measurements to ensure that the swarm density converges to a function
proportional to the scalar field. The boundedness of the domain precludes the
need to impose assumptions on decaying properties of the scalar field at
infinity. Moreover, exponential convergence of the swarm density to the
equilibrium follows from properties of the spectrum of the semigroup generator.
In addition, we use the proposed coverage method to construct a
time-inhomogenous diffusion process and apply the observability of the heat
equation to reconstruct the scalar field over the entire domain from
observations of the robots' random motion over a small subset of the domain. We
verify our results through simulations of the coverage scenario on a 2D domain
and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision
and Control (CDC 2016
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