8,483 research outputs found
Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints
Output feedback controlled synchronization problems for a class of nonlinear
unstable systems under information constraints imposed by limited capacity of
the communication channel are analyzed. A binary time-varying coder-decoder
scheme is described and a theoretical analysis for multi-dimensional
master-slave systems represented in Lurie form (linear part plus nonlinearity
depending only on measurable outputs) is provided. An output feedback control
law is proposed based on the Passification Theorem. It is shown that the
synchronization error exponentially tends to zero for sufficiantly high
transmission rate (channel capacity). The results obtained for synchronization
problem can be extended to tracking problems in a straightforward manner, if
the reference signal is described by an {external} ({exogenious}) state space
model. The results are applied to controlled synchronization of two chaotic
Chua systems via a communication channel with limited capacity.Comment: 8 pages, 2 figure
Controlled Synchronization Under Information Constraints
The class of controlled synchronization systems under information constraints
imposed by limited information capacity of the coupling channel is analyzed. It
is shown that the framework proposed in A. L. Fradkov, B. Andrievsky, R. J.
Evans, Physical Review E 73, 066209 (2006) is suitable not only for
observer-based synchronization but also for controlled master-slave
synchronization via communication channel with limited information capacity. A
simple first order coder-decoder scheme is proposed and a theoretical analysis
for multi-dimensional master-slave systems represented in the Lurie form
(linear part plus nonlinearity depending only on measurable outputs) is
provided. An output feedback control law is proposed based on the Passification
theorem. It is shown that the upper bound of the limit synchronization error is
proportional to the upper bound of the transmission error. As a consequence,
both upper and lower bounds of limit synchronization error are proportional to
the maximum rate of the coupling signal and inversely proportional to the
information transmission rate (channel capacity). The results are applied to
controlled synchronization of two chaotic Chua systems coupled via a controller
and a channel with limited capacity.Comment: 7 pages, 8 figure
Self-synchronization and controlled synchronization
An attempt is made to give a general formalism for synchronization in dynamical systems encompassing most of the known definitions and applications. The proposed set-up describes synchronization of interconnected systems with respect to a set of functionals and captures peculiarities of both self-synchronization and controlled synchronization. Various illustrative examples are give
Dynamics of Oscillators Coupled by a Medium with Adaptive Impact
In this article we study the dynamics of coupled oscillators. We use
mechanical metronomes that are placed over a rigid base. The base moves by a
motor in a one-dimensional direction and the movements of the base follow some
functions of the phases of the metronomes (in other words, it is controlled to
move according to a provided function). Because of the motor and the feedback,
the phases of the metronomes affect the movements of the base while on the
other hand, when the base moves, it affects the phases of the metronomes in
return.
For a simple function for the base movement (such as in which is the velocity of the base,
is a multiplier, is a proportion and and
are phases of the metronomes), we show the effects on the dynamics of the
oscillators. Then we study how this function changes in time when its
parameters adapt by a feedback. By numerical simulations and experimental
tests, we show that the dynamic of the set of oscillators and the base tends to
evolve towards a certain region. This region is close to a transition in
dynamics of the oscillators; where more frequencies start to appear in the
frequency spectra of the phases of the metronomes
Control of the chaotic state caused by the curent-driven ion acoustic instabilit and dynamical behavior using delayed feedback
Controlling chaos caused by the current-driven ion acoustic instability is
attempted using the delayed continuous feedback method, i.e., the time-delay
auto synchronization (TDAS) method introduced by Pyragas [Phys. Lett. A 170
(1992) 421.]. When the control is applied to the typical chaotic state, chaotic
orbit changes to periodic one, maintaining the instability. The chaotic state
is well controlled using the TDAS method. It is found that the control is
achieved when a delay time is chosen near the unstable periodic orbit
corresponding to the fundamental mode. Furthermore, when the delayed feedback
is applied to a periodic nonlinear regime and arbitrary time delay is chosen,
the periodic state is leaded to various motions including chaos. As a related
topic, the synchronization between two instabilities of autonomous discharge
tubes in a glow discharge is studied. Two tubes are settled independently and
interacting each other through the coupler consisted of variable resister and
capacitor. When the value of resister is changed as the strength of coupling,
coupled system shows a state such as chaos synchronization.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004,
Nice (France
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