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1.
This paper deals with the robust fuzzy control for chaotic systems in the
presence of parametric uncertainties. An uncertain Takagi--Sugeno fuzzy model
for a Lorenz chaotic system is first constructed. Then a robust fuzzy state
feedback control scheme ensures the control for stable operations under
bounded parametric uncertainties. For a chaotic system with known
uncertainty bounds, a robust fuzzy regulator is designed by choosing the
control parameters satisfying the linear matrix inequality. To verify the
validity and effectiveness of the proposed controller design method, an
analysis technique is suggested and applied to the control of an uncertain
Lorenz chaotic system. 相似文献
2.
This Letter proposes an adaptive fuzzy bilinear observer (FBO) based synchronization design for generalized Lorenz system (GLS). The GLS can be described to TS fuzzy bilinear generalized Lorenz model (FBGLM) with their states immeasurable and their parameters unknown. We design an adaptive FBO based on TS FBGLM for synchronization. Lyapunov theory is employed to guarantee the stability of error dynamic system via linear matrix equalities (LMIs) and to derive the adaptive laws to estimate unknown parameters. Numerical example is given to demonstrate the validity of our proposed adaptive FBO approach for synchronization. 相似文献
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4.
Vibration caused by friction is harmful to engineering systems. Understanding the mechanism of such a physical phenomenon and developing some strategies to effectively control the vibration have both theoretical and practical significance. Based on our previous work, this paper deals with a problem of active compensation control of friction-induced self-excited vibration using adaptive fuzzy systems. Comparative studies on control performance are carried out, where a class of adaptive compensation control schemes with various friction models are applied to control a motion dynamics with friction. It is observed that our proposed modeling and control techniques are powerful to eliminate the limit cycle and the steady-state error. Furthermore, robustness of the proposed controller with respect to external disturbances is discussed. Simulation results show that the active controller with adaptive fuzzy friction compensation outperforms other active controllers with compensation terms characterized by three well-known friction models. 相似文献
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In this paper, an adaptive fuzzy neural controller (AFNC) for a class of unknown chaotic systems is proposed. The proposed
AFNC is comprised of a fuzzy neural controller and a robust controller. The fuzzy neural controller including a fuzzy neural
network identifier (FNNI) is the principal controller. The FNNI is used for online estimation of the controlled system dynamics
by tuning the parameters of fuzzy neural network (FNN). The Gaussian function, a specific example of radial basis function,
is adopted here as a membership function. So, the tuning parameters include the weighting factors in the consequent part and
the means and variances of the Gaussian membership functions in the antecedent part of fuzzy implications. To tune the parameters
online, the back-propagation (BP) algorithm is developed. The robust controller is used to guarantee the stability and to
control the performance of the closed-loop adaptive system, which is achieved always. Finally, simulation results show that
the AFNC can achieve favourable tracking performances. 相似文献
7.
Yeong-Jeu Sun 《Physics letters. A》2010,374(7):933-1834
In this Letter, the generalized Lorenz chaotic system is considered and the state observation problem of such a system is investigated. Based on the time-domain approach, a simple observer for the generalized Lorenz chaotic system is developed to guarantee the global exponential stability of the resulting error system. Moreover, the guaranteed exponential convergence rate can be correctly estimated. Finally, a numerical example is given to show the effectiveness of the obtained result. 相似文献
8.
A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e. these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. It is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two Quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system. 相似文献
9.
James H. Curry 《Communications in Mathematical Physics》1978,60(3):193-204
A 14-dimensional generalized Lorenz system of ordinary differential equations is constructed and its bifurcation sequence is then studied numerically. Several fundamental differences are found which serve to distinguish this model from Lorenz's original one, the most unexpected of which is a family of invariant two-tori whose ultimate bifurcation leads to a strange attractor. The strange attractor seems to have many of the gross features observed in Lorenz's model and therefore is an excellent candidate for a higher dimensional analogue.On leave from Department of Mathematics, Howard University, Washington, DC, USAThe National Center for Atmospheric Research is sponsored by the National Science Foundation 相似文献
10.
Synchronization of a noise-perturbed generalized Lorenz system by
using sliding mode control method is investigated in this paper. Two
sliding mode control methods are proposed to synchronize the
noise-perturbed generalized Lorenz system. Numerical simulations are
also provided for the illustration and verification of the methods. 相似文献
11.
Based on the Lorenz chaotic system, this paper constructs a new four-dimensional hyperchaotic Lorenz system, and studies the basic dynamic behaviours of the system. The Routh--Hurwitz theorem is applied to derive the stability conditions of the proposed system. Furthermore, based on Lyapunov stability theory, an adaptive controller is designed and the new four-dimensional hyperchaotic Lorenz system is controlled at equilibrium point. Numerical simulation results are presented to illustrate the effectiveness of this method. 相似文献
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13.
A chaotic system is bounded, and its trajectory is confined
to a certain region which is called the chaotic attractor. No matter how
unstable the interior of the system is, the trajectory never
exceeds the chaotic attractor. In the present paper, the sphere
bound of the generalized Lorenz system is given, based on the
Lyapunov function and the Lagrange multiplier method. Furthermore, we
show the actual parameters and perform numerical simulations. 相似文献
14.
Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated. 相似文献
15.
<正>This paper presents a robust output feedback control method for uncertain chaotic systems,which comprises a nonlinear inversion-based controller with a fuzzy robust compensator.The proposed controller eliminates the unknown nonlinear function by using a fuzzy system,whose inputs are not the state variables but feedback error signals.The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique.The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems.Theoretical results are illustrated through two simulation examples. 相似文献
16.
The projection of the chaotic attractor observed from the Lorenz system in the
$X$--$Z$ plane is like a butterfly, hence the classical Lorenz system is widely
known as the butterfly attractor, and has served as a prototype model for studying
chaotic behaviour since it was coined.In this work we take one step further to
investigate some fundamental dynamic behaviours of a novel hybrid Takagi--Sugeno
(TS) fuzzy Lorenz-type system, which is essentially derived from the
delta-operator-based TS fuzzy modelling for complex nonlinear systems, and contains
the original Lorenz system of continuous-time TS fuzzy form as a special case. By
simply and appropriately tuning the additional parametric perturbations in the
two-rule hybrid TS fuzzy Lorenz-type system, complex (two-wing) butterfly attractors
observed from this system in the three dimensional (3D) $X$--$Y$--$Z$ space are
created, which have not yet been reported in the literature, and the forming
mechanism of the compound structures have been numerically investigated. 相似文献
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18.
A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs 下载免费PDF全文
Mohammad Pourmahmood Aghababa 《中国物理 B》2011,20(9):90505-090505
In this paper, the problem of the finite-time synchronization of two uncertain chaotic gyros is discussed. The parameters of both the master and the slave gyros are assumed to be unknown in advance. The effects of model uncertainties and input nonlinearities are also taken into account. An appropriate adaptation law is proposed to tackle the gyros' unknown parameters. Based on the adaptation law and the finite-time control technique, proper control laws are introduced to ensure that the trajectories of the slave gyro converge to the trajectories of the master gyro in a given finite time. Simulation results show the applicability and the efficiency of the proposed finite-time controller. 相似文献
19.
《Physics letters. A》1997,226(6):349-354
We study impulsive synchronization of two Lorenz systems. In an impulsive synchronization scheme, driving signals are transmitted to the driven system at discrete instants. The driven system changes its state variables instantaneously at these discrete instants according to synchronization errors. An asymptotically stable impulsive synchronization scheme is presented. The boundaries of stable regions of impulsive synchronization are also presented. Computer simulation results are given. 相似文献