Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scalin...Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.展开更多
This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unkno...This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic L/i system is used to illustrate the validity of this theoretic method.展开更多
In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-la...In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.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
针对炉温类被控对象提出了一种基于开环阶跃响应的获取对象特征参数的新方法,给出了程序流程图。与两点法、交叉两点法及特征面积法等方法不同,在应用计算机求解的过程中仅需保留邻近4个采样时刻的采样值,且无需阶跃响应达到稳态即可计...针对炉温类被控对象提出了一种基于开环阶跃响应的获取对象特征参数的新方法,给出了程序流程图。与两点法、交叉两点法及特征面积法等方法不同,在应用计算机求解的过程中仅需保留邻近4个采样时刻的采样值,且无需阶跃响应达到稳态即可计算出对象的特征参数,具有数据存储量小、速度快、方法简单等特点。应用该方法获取某红外线加热炉温度系统的特征参数,并采用ITAE(Integral Time Absolute Error)设定公式整定PID控制器的参数,取得了较好的控制效果。展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11371049)the Science Foundation of Beijing Jiaotong University(Grant Nos.2011JBM130 and 2011YJS076)
文摘Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.
基金Project supported by the Natural Science Foundation of Hebei Province,China (Grant No.A2010000343)
文摘This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic L/i system is used to illustrate the validity of this theoretic method.
基金The project is supported by NSF of Anhui Province(No.2005jk218), China.
文摘In this paper, we present an explicit one-step method for solving periodic initial value problems of second order ordinary differential equations. The method is P-stable, and of first algebraic order and high phase-lag order. To improve the algebraic order, we give a composition second order scheme with the proposed method and its adjoint. We report some numerical results to illustrate the efficiency of our methods.
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.
文摘针对炉温类被控对象提出了一种基于开环阶跃响应的获取对象特征参数的新方法,给出了程序流程图。与两点法、交叉两点法及特征面积法等方法不同,在应用计算机求解的过程中仅需保留邻近4个采样时刻的采样值,且无需阶跃响应达到稳态即可计算出对象的特征参数,具有数据存储量小、速度快、方法简单等特点。应用该方法获取某红外线加热炉温度系统的特征参数,并采用ITAE(Integral Time Absolute Error)设定公式整定PID控制器的参数,取得了较好的控制效果。
