In this paper we present an adaptive scheme to achieve lag synchronization for uncertain dynamical systems with time delays and unknown parameters. In contrast to the nonlinear feedback scheme reported in the previous...In this paper we present an adaptive scheme to achieve lag synchronization for uncertain dynamical systems with time delays and unknown parameters. In contrast to the nonlinear feedback scheme reported in the previous literature, the proposed controller is a linear one which only involves simple feedback information from the drive system with signal popagation lags. Besides, the unknown parameters can also be identified via the proposed updating laws in spite of the existence of model delays and transmission lags, as long as the linear independence condition between the related function elements is satisfied. Two examples, i.e., the Mackey-Glass model with single delay and the Lorenz system with multiple delays, are employed to show the effectiveness of this approach. Some robustness issues are also discussed, which shows that the proposed scheme is quite robust in switching and noisy environment.展开更多
This paper investigates robust unified （lag, anticipated, and complete） synchronization of two coupled chaotic systems, By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and ...This paper investigates robust unified （lag, anticipated, and complete） synchronization of two coupled chaotic systems, By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.展开更多
In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive d...In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive differential equations, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level. The idea and approach developed in this paper can provide a more practical framework for the synchronization between identical and different chaotic systems in parameter perturbation circumstances. Simulation results finally demonstrate the effectiveness of the method.展开更多
Active control is an effective method for synchronizing two identical chaotic systems. However, this method works only for a certain class of chaotic systems with known parameters. An improvement method was proposed i...Active control is an effective method for synchronizing two identical chaotic systems. However, this method works only for a certain class of chaotic systems with known parameters. An improvement method was proposed in order to overcome this limitation in this paper. A classical example was used to demonstrate the method. Finally, numerical examples were given to validate the efficiency of the method.展开更多
In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impu...In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.展开更多
Conditions for complete and lag synchronizations in drive-response systems are considered under the unified framework of generalized synchronization. The question is addressed that whether the synchronization conditio...Conditions for complete and lag synchronizations in drive-response systems are considered under the unified framework of generalized synchronization. The question is addressed that whether the synchronization conditions achieving complete synchronization is still valid for lag synchronization when the time delay of signal transmission between the drive and response systems increases from 0. Theoretical and numerical results show that whether the synchronization conditions is stable for the influence of the time delay of signal transmission depends on a particular form of equilibria of the drive and response systems. Furthermore, it seems that the less the number of the equilibria of the drive system, the more likely the synchronization conditions are stable for the time delay of signal trans- mission.展开更多
The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinea...The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.展开更多
In this paper, we study the chaotic behaviors in a fractional order logistic delay system. We find that chaos exists in the fractional order logistic delay system with an order being less than 1. In addition, we numer...In this paper, we study the chaotic behaviors in a fractional order logistic delay system. We find that chaos exists in the fractional order logistic delay system with an order being less than 1. In addition, we numerically simulate the continuances of the chaotic behaviors in the logistic delay system with orders from 0.1 to 0.9. The lowest order we find to have chaos in this system is 0.1. Then we further investigate two methods in controlling the fractional order chaotic logistic delay system based on feedback. Finally, we investigate a lag synchronization scheme in this system. Numerical simulations show the effectiveness and feasibility of our approach.展开更多
基金supported by the National Science and Technology Major Project,China(Grant No.2011ZX03005-002)the Shandong Academy of Science Development Fund for Science and Technology,Chinathe Pilot Project for Science and Technology in Shandong Academy of Sciences,China
文摘In this paper we present an adaptive scheme to achieve lag synchronization for uncertain dynamical systems with time delays and unknown parameters. In contrast to the nonlinear feedback scheme reported in the previous literature, the proposed controller is a linear one which only involves simple feedback information from the drive system with signal popagation lags. Besides, the unknown parameters can also be identified via the proposed updating laws in spite of the existence of model delays and transmission lags, as long as the linear independence condition between the related function elements is satisfied. Two examples, i.e., the Mackey-Glass model with single delay and the Lorenz system with multiple delays, are employed to show the effectiveness of this approach. Some robustness issues are also discussed, which shows that the proposed scheme is quite robust in switching and noisy environment.
基金Project supported by the National Natural Science Foundation of China （Grant No 10372054）.
文摘This paper investigates robust unified （lag, anticipated, and complete） synchronization of two coupled chaotic systems, By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.
基金Project supported by the National Natural Science foundation of China (Grant Nos 60534010, 60572070, 60774048 and 60728307)the Program for Changjiang Scholars and Innovative Research Team in University (Grant No 60521003) the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)
文摘In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive differential equations, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level. The idea and approach developed in this paper can provide a more practical framework for the synchronization between identical and different chaotic systems in parameter perturbation circumstances. Simulation results finally demonstrate the effectiveness of the method.
文摘Active control is an effective method for synchronizing two identical chaotic systems. However, this method works only for a certain class of chaotic systems with known parameters. An improvement method was proposed in order to overcome this limitation in this paper. A classical example was used to demonstrate the method. Finally, numerical examples were given to validate the efficiency of the method.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006 and 60521003)the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)+2 种基金Liaoning Provincial Natural Science Foundation of China (Grant No 20062018)State Key Development Program for Basic research of China (Grant No 2009CB320601)111 Project,China (Grant No B08015)
文摘In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.
基金supported by the National Natural Science Foundation of China(11002103 and 11032009)Shanghai Leading Academic Discipline(B302)
文摘Conditions for complete and lag synchronizations in drive-response systems are considered under the unified framework of generalized synchronization. The question is addressed that whether the synchronization conditions achieving complete synchronization is still valid for lag synchronization when the time delay of signal transmission between the drive and response systems increases from 0. Theoretical and numerical results show that whether the synchronization conditions is stable for the influence of the time delay of signal transmission depends on a particular form of equilibria of the drive and response systems. Furthermore, it seems that the less the number of the equilibria of the drive system, the more likely the synchronization conditions are stable for the time delay of signal trans- mission.
文摘The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.
文摘In this paper, we study the chaotic behaviors in a fractional order logistic delay system. We find that chaos exists in the fractional order logistic delay system with an order being less than 1. In addition, we numerically simulate the continuances of the chaotic behaviors in the logistic delay system with orders from 0.1 to 0.9. The lowest order we find to have chaos in this system is 0.1. Then we further investigate two methods in controlling the fractional order chaotic logistic delay system based on feedback. Finally, we investigate a lag synchronization scheme in this system. Numerical simulations show the effectiveness and feasibility of our approach.
