共查询到20条相似文献,搜索用时 161 毫秒
1.
Mohammad Pourmahmood Aghababa 《Communications in Nonlinear Science & Numerical Simulation》2012,17(6):2670-2681
This paper proposes a novel fractional-order sliding mode approach for stabilization and synchronization of a class of fractional-order chaotic systems. Based on the fractional calculus a stable integral type fractional-order sliding surface is introduced. Using the fractional Lyapunov stability theorem, a single sliding mode control law is proposed to ensure the existence of the sliding motion in finite time. The proposed control scheme is applied to stabilize/synchronize a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. Some numerical simulations are performed to confirm the theoretical results of the paper. It is worth noticing that the proposed fractional-order sliding mode controller can be applied to control a broad range of fractional-order dynamical systems. 相似文献
2.
One new theorem for Caputo fractional derivative and two new theorems for Caputo fractional order systems, when 1 a 2, are proposed in this paper. The results have proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the instability and the stability of many fractional order systems,which can be nonlinear and time varying. 相似文献
3.
利用分数维微积分(Fractional Calculus,简记为FC)理论,推广了Lyapunov第二方法,得到了类Lyapunov判据,给出了一种新的构造Lyapunov函数的方法和途径,并且把此判据推广到分数维系统,给出了一种分数维系统的Lyapunov稳定性问题的判别方法. 相似文献
4.
Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty 总被引:1,自引:0,他引:1
Sara DadrasHamid Reza Momeni 《Communications in Nonlinear Science & Numerical Simulation》2012,17(1):367-377
A novel type of control strategy combining the fractional calculus with terminal sliding mode control called fractional terminal sliding mode control is introduced for a class of dynamical systems subject to uncertainties. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. The proposed fractional-order terminal sliding mode controller ensures the finite time stability of the closed-loop system. Finally, numerical simulation results are presented and compared to illustrate the effectiveness of the proposed method. 相似文献
5.
This paper presents a new fractional-order hyperchaotic system. The chaotic behaviors of this system in phase portraits are analyzed by the fractional calculus theory and computer simulations. Numerical results have revealed that hyperchaos does exist in the new fractional-order four-dimensional system with order less than 4 and the lowest order to have hyperchaos in this system is 3.664. The existence of two positive Lyapunov exponents further verifies our results. Furthermore, a novel modified generalized projective synchronization (MGPS) for the fractional-order chaotic systems is proposed based on the stability theory of the fractional-order system, where the states of the drive and response systems are asymptotically synchronized up to a desired scaling matrix. The unpredictability of the scaling factors in projective synchronization can additionally enhance the security of communication. Thus MGPS of the new fractional-order hyperchaotic system is applied to secure communication. Computer simulations are done to verify the proposed methods and the numerical results show that the obtained theoretic results are feasible and efficient. 相似文献
6.
7.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(6):2656-2657
In this note some points to paper [L. Pan, W. Zhou, J. Fang, D. Li, Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762] are presented. Hereby, we illustrate that the way that authors in [1] treat with fractional version of Lyapunov stability theorem suffers lack of a correct justification. 相似文献
8.
Shiva Eshaghi Reza Khoshsiar Ghaziani Alireza Ansari 《Mathematical Methods in the Applied Sciences》2019,42(7):2302-2323
In this paper, we studied the stabilization of nonlinear regularized Prabhakar fractional dynamical systems without and with time delay. We establish a Lyapunov stabiliy theorem for these systems and study the asymptotic stability of these systems without design a positive definite function V (without considering the fractional derivative of function V is negative). We design a linear feedback controller to control and stabilize the nonautonomous and autonomous chaotic regularized Prabhakar fractional dynamical systems without and with time delay. By means of the Lyapunov stability, we obtain the control parameters for these type of systems. We further present a numerical method to solve and analyze regularized Prabhakar fractional systems. Furthermore, by employing numerical simulation, we reveal chaotic attractors and asymptotic stability behaviors for four systems to illustrate the presented theorem. 相似文献
9.
研究了一类分数阶金融系统的混沌同步问题,基于Lyapunov稳定性理论和分数阶微积分的相关理论,给出了两种实现同步的控制方案,仿真算例表明了方法的有效性. 相似文献
10.
Surendra Kumar 《Journal of Optimization Theory and Applications》2017,174(1):108-121
This paper considers fractional optimal control of a semilinear system with fixed delay in a reflexive Banach space. The existence and uniqueness of mild solution are obtained using the Weissinger’s fixed point theorem. The existence of optimal control for the system governed by fractional-order semilinear equation with fixed delay in state is presented. To show the effectiveness of the developed theory, an example is given. 相似文献
11.
《Chaos, solitons, and fractals》2006,27(2):519-525
In this paper, a drive-response synchronization method with linear output error feedback is presented for synchronizing a class of fractional-order chaotic systems via a scalar transmitted signal. Based on stability theory of fractional-order systems and linear system theory, a necessary and sufficient condition for the existence of the feedback gain vector such that global synchronization between the fractional-order drive system and response system can be achieved and its design method are given. This synchronization approach that is simple, global and theoretically rigorous enables synchronization of fractional-order chaotic systems be achieved in a systematic way and does not require the computation of the conditional Lyapunov exponents. An example is used to illustrate the effectiveness of the proposed synchronization method. 相似文献
12.
13.
Vajiheh Vafaei Hossein Kheiri Aliasghar Jodayree Akbarfam 《Mathematical Methods in the Applied Sciences》2019,42(8):2761-2773
In this paper, a novel fractional‐integer integral type sliding mode technique for control and generalized function projective synchronization of different fractional‐order chaotic systems with different dimensions in the presence of disturbances is presented. When the upper bounds of the disturbances are known, a sliding mode control rule is proposed to insure the existence of the sliding motion in finite time. Furthermore, an adaptive sliding mode control is designed when the upper bounds of the disturbances are unknown. The stability analysis of sliding mode surface is given using the Lyapunov stability theory. Finally, the results performed for synchronization of three‐dimensional fractional‐order chaotic Hindmarsh‐Rose (HR) neuron model and two‐dimensional fractional‐order chaotic FitzHugh‐Nagumo (FHN) neuron model. 相似文献
14.
This article is devoted to the study of nonlinear fractional Schrödinger equation with a Gaussian nonlocal response. We firstly prove the existence of solitary wave solutions by using the variational method and Mountain Pass Theorem. Numerical simulations are presented to verify the findings of the existence theorem. And we also investigate the impacts of Gaussian nonlocal response and fractional-order derivatives on the solitary waves, which enable us to perform control experiments for the development of rogue waves in quantum mechanics and optics. 相似文献
15.
Mohammad Pourmahmood Aghababa 《Complexity》2016,21(6):224-233
This article deals with the problem of control of canonical non‐integer‐order dynamical systems. We design a simple dynamical fractional‐order integral sliding manifold with desired stability and convergence properties. The main feature of the proposed dynamical sliding surface is transferring the sign function in the control input to the first derivative of the control signal. Therefore, the resulted control input is smooth and without any discontinuity. So, the harmful chattering, which is an inherent characteristic of the traditional sliding modes, is avoided. We use the fractional Lyapunov stability theory to derive a sliding control law to force the system trajectories to reach the sliding manifold and remain on it forever. A nonsmooth positive definite function is applied to prove the existence of the sliding motion in a given finite time. Some computer simulations are presented to show the efficient performance of the proposed chattering‐free fractional‐order sliding mode controller. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–233, 2016 相似文献
16.
17.
18.
Chaotic fractional‐order model for muscular blood vessel and its control via fractional control scheme 下载免费PDF全文
This article studies the chaotic and complex behavior in a fractional‐order biomathematical model of a muscular blood vessel (MBV). It is shown that the fractional‐order MBV (FOMBV) model exhibits very complex and rich dynamics such as chaos. We show that the corresponding maximal Lyapunov exponent of the FOMBV system is positive which implies the existence of chaos. Strange attractors of the FOMBV model are depicted to validate the chaotic behavior of the system. We change the fractional order of the model and investigate the dynamics of the system. To suppress the chaotic behavior of the model, we propose a single input fractional finite‐time controller and prove its stability using the fractional Lyapunov theory. In addition, the effects of the model uncertainties and external disturbances are taken into account and a robust fractional finite‐time controller is constructed. The upper bound of the chaos suppression time is also given. Some computer simulations are presented to illustrate the findings of this article. © 2014 Wiley Periodicals, Inc. Complexity 20: 37–46, 2014 相似文献
19.
The stability results which comprise the Direct Method of Lyapunov involve the existence of auxiliary functions (Lyapunov functions) endowed with certain definiteness properties. Although the Direct Method is very general and powerful, it has some limitations: there are dynamical systems with known stability properties for which there do not exist Lyapunov functions which satisfy the hypotheses of a Lyapunov stability theorem.In the present paper we identify a scalar switched dynamical system whose equilibrium (at the origin) has known stability properties (e.g., uniform asymptotic stability) and we prove that there does not exist a Lyapunov function which satisfies any one of the Lyapunov stability theorems (e.g., the Lyapunov theorem for uniform asymptotic stability). Using this example as motivation, we establish stability results which eliminated some of the limitations of the Direct Method alluded to. These results involve time-averaged Lyapunov function derivatives (TALFD’s). We show that these results are amenable to the analysis of the same dynamical systems for which the Direct Method fails. Furthermore, and more importantly, we prove that the stability results involving TALFD’s are less conservative than the results which comprise the Direct Method (which henceforth, we refer to as the classical Lyapunov stability results).While we confine our presentation to continuous finite-dimensional dynamical systems, the results presented herein can readily be extended to arbitrary continuous dynamical systems defined on metric spaces. Furthermore, with appropriate modifications, stability results involving TALFD’s can be generalized to discontinuous dynamical systems (DDS). 相似文献
20.
Yongshun Zhao Shurong Sun Yongxiang Zhang 《Journal of Applied Mathematics and Computing》2017,53(1-2):183-199
In this paper, we investigate existence and generalized Hyers–Ulam–Rassias stability of Stieltjes quadratic functional integral equations. Firstly, we show some basic properties of the composite function of bounded variation. Secondly, we derive the generalized Hyers–Ulam–Rassias stability result after examining the existence and uniqueness results via the theory of measure of noncompactness and a fixed point theorem of Darbo type. Finally, two examples of functional integral equations of fractional order are given to demonstrate the applicability of our results. 相似文献