This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition ...This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.展开更多
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to ac...This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the ...To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the Mittag-Lefler function,Laplace transform and Gronwall inequality,a linear stabilizing controller is derived,which uses the fractional order of the delayed system and the upper bound of system nonlinear functions.In the second method,at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality(LMI)which can easily be solved.Then,on the basis of this result,a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds.Simulation results show the effectiveness of the proposed methods.展开更多
In this paper, by utilizing the fractional calculus theory and computer simulations, dynamics of the fractional order system is studied. Further, we have extended the nonlinear feedback control in ODE systems to fract...In this paper, by utilizing the fractional calculus theory and computer simulations, dynamics of the fractional order system is studied. Further, we have extended the nonlinear feedback control in ODE systems to fractional order systems, in order to eliminate the chaotic behavior. The results are proved analytically by stability condition for fractional order system. Moreover numerical simulations are shown to verify the effectiveness of the proposed control scheme.展开更多
In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on ...In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.展开更多
This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict...This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.展开更多
This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing ...This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.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
In this article,the problem of event-triggered adaptive fuzzy finite time control of nonstrict feedback fractional order nonlinear systems is investigated.By using the property of fuzzy basis function,the obstacle cau...In this article,the problem of event-triggered adaptive fuzzy finite time control of nonstrict feedback fractional order nonlinear systems is investigated.By using the property of fuzzy basis function,the obstacle caused by algebraic loop problems is successfully circumvented.Moreover,a new adaptive event-triggered scheme is designed under the unified framework of backstepping control method,which can largely reduce the amount of communications.The stability of the closed-loop system is ensured through fractional Lyapunov stability analysis.Finally,the effectiveness of the proposed scheme is verified by simulation examples.展开更多
This paper focuses on the comparative analysis of bifurcation control approaches for a fractional-order delayed predator-prey system. The state feedback schemes with and without time delay are dexterously designed dur...This paper focuses on the comparative analysis of bifurcation control approaches for a fractional-order delayed predator-prey system. The state feedback schemes with and without time delay are dexterously designed during the bifurcation control for the proposed system, and the comparative study is elaborately performed on bifurcation control theoretically. The salient feature of the current paper is that the analysis of time of bifurcation control for the proposed system is investigated based on various state feedback control strategies. Analysis reveals that the feedback control approach without time delay overly outmatches the one with time delay for bifurcation control in the considered systems so long as the uniform feedback gain is selected. It consumes less time to control bifurcation while utilizing the first controller in comparison with the second one. Numerical examples are ultimately employed to confirm the correctness of the theoretical results.展开更多
The current paper deals with synchronization problem among chaotic nonlinear fractional order systems considering input saturation constraint.To develop the idea,at first a generalized sector condition and a memory-le...The current paper deals with synchronization problem among chaotic nonlinear fractional order systems considering input saturation constraint.To develop the idea,at first a generalized sector condition and a memory-less nonlinear function are employed to deal with the saturation problem.Then a new state feedback controller is designed to achieve synchronization in master-slave chaotic fractional order nonlinear systems with input saturation.Using the state feedback controller,the asymptotic stability of whole dynamic error model between master and slave is achieved.The stability of the closed-loop system is guaranteed using Lyapunov theory and sufficient stability conditions are formulated in terms of caputo fractional derivative of a quadratic Lyapunov function and Linear Matrix Inequalities(LMI).Finally,to verify the effectiveness of the proposed control scheme,some simulation results are employed to show the effectiveness of the proposed methodology.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 60702023)Natural Science Foundation of Zhejiang Province (Grant No. Y107440)
文摘This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.
文摘This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
文摘To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the Mittag-Lefler function,Laplace transform and Gronwall inequality,a linear stabilizing controller is derived,which uses the fractional order of the delayed system and the upper bound of system nonlinear functions.In the second method,at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality(LMI)which can easily be solved.Then,on the basis of this result,a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds.Simulation results show the effectiveness of the proposed methods.
文摘In this paper, by utilizing the fractional calculus theory and computer simulations, dynamics of the fractional order system is studied. Further, we have extended the nonlinear feedback control in ODE systems to fractional order systems, in order to eliminate the chaotic behavior. The results are proved analytically by stability condition for fractional order system. Moreover numerical simulations are shown to verify the effectiveness of the proposed control scheme.
基金supported by the Natural Science Foundation of Hebei Province,China(Grant No.A2010000343)
文摘In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.
文摘This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.
基金joint financial support of Thailand Research Fund RSA 6280004,RUSA-Phase 2.0 Grant No.F 24-51/2014-UPolicy(TN Multi-Gen),Dept.of Edn.Govt.of India,UGC-SAP(DRS-I)Grant No.F.510/8/DRS-I/2016(SAP-I)+1 种基金DST(FIST-level I)657876570 Grant No.SR/FIST/MS-I/2018/17Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics(NAMAM)group number RG-DES-2017-01-17。
文摘This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.
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.
基金the Funds of National Science of China under Grant Nos.61973146 and 61773188in part by the Distinguished Young Scientific Research Talents Plan in Liaoning Province under Grant Nos.XLYC1907077 and JQL201915402。
文摘In this article,the problem of event-triggered adaptive fuzzy finite time control of nonstrict feedback fractional order nonlinear systems is investigated.By using the property of fuzzy basis function,the obstacle caused by algebraic loop problems is successfully circumvented.Moreover,a new adaptive event-triggered scheme is designed under the unified framework of backstepping control method,which can largely reduce the amount of communications.The stability of the closed-loop system is ensured through fractional Lyapunov stability analysis.Finally,the effectiveness of the proposed scheme is verified by simulation examples.
基金supported by the Nanhu Scholars Program for Young Scholars of XYNU
文摘This paper focuses on the comparative analysis of bifurcation control approaches for a fractional-order delayed predator-prey system. The state feedback schemes with and without time delay are dexterously designed during the bifurcation control for the proposed system, and the comparative study is elaborately performed on bifurcation control theoretically. The salient feature of the current paper is that the analysis of time of bifurcation control for the proposed system is investigated based on various state feedback control strategies. Analysis reveals that the feedback control approach without time delay overly outmatches the one with time delay for bifurcation control in the considered systems so long as the uniform feedback gain is selected. It consumes less time to control bifurcation while utilizing the first controller in comparison with the second one. Numerical examples are ultimately employed to confirm the correctness of the theoretical results.
文摘The current paper deals with synchronization problem among chaotic nonlinear fractional order systems considering input saturation constraint.To develop the idea,at first a generalized sector condition and a memory-less nonlinear function are employed to deal with the saturation problem.Then a new state feedback controller is designed to achieve synchronization in master-slave chaotic fractional order nonlinear systems with input saturation.Using the state feedback controller,the asymptotic stability of whole dynamic error model between master and slave is achieved.The stability of the closed-loop system is guaranteed using Lyapunov theory and sufficient stability conditions are formulated in terms of caputo fractional derivative of a quadratic Lyapunov function and Linear Matrix Inequalities(LMI).Finally,to verify the effectiveness of the proposed control scheme,some simulation results are employed to show the effectiveness of the proposed methodology.
