|
FrB1 Regular
Session |
C101
|
Networks
and Detection |
|
|
Chair: Acho, Leonardo |
EUETIB-Univ. Pol. of Catalunya |
Co-Chair: Proskurnikov,
Anton |
St.-Petersburg State Univ. |
|
14:30-14:50, Paper
FrB1.1 |
|
The Circle Criterion for Synchronization
in Nonlinearly Coupled Networks |
Proskurnikov, Anton |
St.-Petersburg State Univ. |
Keywords:
Absolute
Stability, Complex
Network, Anti-Control
and Synchronization
Abstract: The problem of
synchronization (consensus) in nonlinearly coupled
network is addressed. The agents of the network are
assumed to identical and linear, however, they may
have arbitrary order and be unstable. The interaction
topology may switch and the couplings are uncertain,
assumed only to satisfy conventional quadratic
constraints. We offer easily verifiable
synchronization criteria, based on the
Kalman-Yakubovich-Popov lemma and extending a number
of known result for agents with special dynamics.
Those criteria are close in spirit to the celebrated
circle criterion for the stability of Lurie systems.
|
|
14:50-15:10, Paper
FrB1.2 |
|
Practical and Robust Synchronization of
Systems with Additive Linear Uncertainties |
Montenbruck, Jan Maximilian |
Univ. of Stuttgart |
Seyboth, Georg S. |
Univ. of Stuttgart |
Allgower, Frank |
Univ. of Stuttgart |
Keywords:
Anti-Control
and Synchronization, Nonlinear
Cooperative Control, Lyapunov
Methods
Abstract: We investigate the
synchronization of systems with additive
uncertainties. In doing so, we establish a setup of
diffusively coupled nonlinear systems that are
perturbed by unknown linear functions, each. By
assuming bounded solutions of the nominal uncoupled
systems, we derive sufficient conditions for
boundedness of the solutions of the coupled systems
with uncertainties. Next, using the QUAD condition, we
derive conditions for the synchronization error to
remain bounded. Subsequently, we investigate the
impact of the coupling strength on this bound and find
that the bound can be made arbitrarily small for
sufficiently large gains, thus establishing criteria
for practical synchronization. Finally, we consider
classes of uncertainties which consist of matrices
whose maximal singular value is smaller than a
specific value and show practical synchronization for
all uncertainties belonging to that class. Therefore,
we establish conditions for robust synchronization
with respect to such a class. Our theoretical results
are validated with a numerical example composed of
perturbed Van der Pol oscillators.
|
|
15:10-15:30, Paper
FrB1.3 |
|
A Chaotic Secure Communication Scheme
Based on Duffing Oscillators and Frequency
Estimation |
Zapateiro, Mauricio |
Univ. Pol. de Catalunya |
Vidal, Yolanda |
Univ. Pol. de Catalunya |
Acho, Leonardo |
EUETIB-Univ. Pol. of Catalunya |
Keywords:
Lyapunov
Methods, Chaos
Control, Applications
of Observer Design
Abstract: This work presents a new
technique to securely transmit and retrieve a message
signal via chaotic systems. In our system, a
two-valued message signal modulates the frequency of a
Duffing oscillator sinusoidal term. An observer is
used in the receiver side to retrieve the sinusoidal
signal that contains the message and a novel frequency
estimator is then used to reproduce an approximated
estimation of the message signal. The performance of
the system is analyzed by means of numerical
simulations performed in Matlab.
|
|
15:30-15:50, Paper
FrB1.4 |
|
A Cluster Control of Nonlinear Network
Systems with External Inputs |
Ryono, Koki |
Tokyo Metropolitan Univ. |
Oguchi, Toshiki |
Tokyo Metropolitan Univ. |
Keywords:
Chaos
Control, Complex
Network, Bifurcation
and Chaos
Abstract: In this paper, we consider
the synchronization problem in networks of identical
nonlinear systems with delayed couplings and external
inputs. We show that the existence of external inputs
can generate partial synchronization in networks and
the synchronization pattern based on the notion of
equitable partitions. Some illustrated examples with
numerical simulation are given to verify the validity
of the result obtained in this paper. The result
indicates that synchronization patterns can be
controlled by applying external inputs.
|
|
15:50-16:10, Paper
FrB1.5 |
|
Outlier Detection for Polynomial Systems
Using Semidefinite Relaxations |
Borchers, Steffen |
Max Planck Inst. for dynamics of complex
Tech. systems |
Findeisen, Rolf |
Otto-von-Guericke-Univ. Magdeburg |
Keywords:
Fault
Detection, State
Estimation and Applications, Parameter
Estimation
Abstract: Outlier detection and
analysis is a primary step in modelling towards
obtaining unbiased estimates, model validation, and
coherent analysis, because outliers may contain
valuable information or lead to falsely rejecting
hypotheses. In this work, we describe approaches for
detecting outliers in measurements due to
time-dependent and possibly non-homogeneously
distributed measurement uncertainties within a
set-membership setting. We propose a combinatorial
outlier detection approach based on a rigorous
invalidity criterion using semidefinite programming
relaxations. To overcome combinatorial complexity
issues, we furthermore propose a reachability-based
approach to identify outlier candidates, which can be
easily verified thereafter.
|
|
16:10-16:30, Paper
FrB1.6 |
|
Chaotic Behavior of the Folding Map on the
Equilateral Triangle |
Ishikawa, Tetsuya |
Tokyo Inst. of Tech. |
Hayakawa, Tomohisa |
Tokyo Inst. of Tech. |
Keywords:
Bifurcation
and Chaos
Abstract: In recent years, it becomes
important to understand chaotic behaviors in order to
analyze nonlinear dynamics because chaotic behavior
can be observed in many models in the field of
physics, biology, and so on. To understand chaotic
behaviors, investigating mechanisms of chaos is
necessary and it is meaningful to study simple models
that shows chaotic behaviors. In this paper, we
propose an extremely simple triangle folding map and
show that the map has k-periodic points for any
integer k, and show the map has sensitivity to initial
conditions. Finally, we discuss the connection with
the Sierpinski gasket and construct similar types of
fractal geometry.
|