6,239 research outputs found
Synchronization of chaotic systems using time-delayed fuzzy state-feedback controller
This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, T-S fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. A simulation example is presented to illustrate the merits of the proposed approach
Synchronization problems for unidirectional feedback coupled nonlinear systems
In this paper we consider three different synchronization problems consisting
in designing a nonlinear feedback unidirectional coupling term for two
(possibly chaotic) dynamical systems in order to drive the trajectories of one
of them, the slave system, to a reference trajectory or to a prescribed
neighborhood of the reference trajectory of the second dynamical system: the
master system. If the slave system is chaotic then synchronization can be
viewed as the control of chaos; namely the coupling term allows to suppress the
chaotic motion by driving the chaotic system to a prescribed reference
trajectory. Assuming that the entire vector field representing the velocity of
the state can be modified, three different methods to define the nonlinear
feedback synchronizing controller are proposed: one for each of the treated
problems. These methods are based on results from the small parameter
perturbation theory of autonomous systems having a limit cycle, from nonsmooth
analysis and from the singular perturbation theory respectively. Simulations to
illustrate the effectiveness of the obtained results are also presented.Comment: To appear in Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Ana
Adaptive sliding mode observers in uncertain chaotic cryptosystems with a relaxed matching condition
We study the performance of adaptive sliding mode observers in chaotic synchronization and communication in the presence of uncertainties. The proposed robust adaptive observer-based synchronization is used for cryptography based on chaotic masking modulation (CM). Uncertainties are intentionally injected into the chaotic dynamical system to achieve higher security and we use robust sliding mode observer design methods for the uncertain nonlinear dynamics. In addition, a relaxed matching condition is introduced to realize the robust observer design. Finally, a Lorenz system is employed as an illustrative example to demonstrate the effectiveness and feasibility of the proposed cryptosyste
Optimum PID Control of Multi-wing Attractors in A Family of Lorenz-like Chaotic Systems
Multi-wing chaotic attractors are highly complex nonlinear dynamical systems
with higher number of index-2 equilibrium points. Due to the presence of
several equilibrium points, randomness of the state time series for these
multi-wing chaotic systems is higher than that of the conventional double wing
chaotic attractors. A real coded Genetic Algorithm (GA) based global
optimization framework has been presented in this paper, to design optimum PID
controllers so as to control the state trajectories of three different
multi-wing Lorenz like chaotic systems viz. Lu, Rucklidge and Sprott-1 system.Comment: 6 pages, 21 figures; 2012 Third International Conference on
Computing, Communication and Networking Technologies (ICCCNT'12), July 2012,
Coimbator
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
On synchronization of chaotic systems
This paper deals with the problem of synchronization, or observer design, of chaotic dynamical systems. It is argued that the complex nature of the transmitter dynamics may provide additional tools for finding a suitable observer. A number of characteristic examples illustrate the idea, and reveal some challenging open problems in this contex
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