一种新的分数阶混沌系统研究

为了提高混沌信号的复杂性,提出一个新的分数阶混沌系统.介绍两种分数阶微积分的分析方法,时域求解法对其进行数值仿真;时频域转换法对其进行电路仿真.数值仿真结果表明,系统存在混沌的最低阶数是2.31.设计该系统的分数阶混沌振荡电路,电路仿真与数值仿真结果相符,证实了该分数阶混沌振荡电路的可行性.     

基于Lyapunov方程的分数阶混沌系统投影同步

针对阶次小于1的分数阶混沌系统,结合Lyapunov方程的稳定性判定理论,实现了一类分数阶混沌系统的投影同步控制。通过该方法,保留部分了非线性项,改善混沌投影同步的性能,并从理论上证明了该方案的可行性。     

分数阶混沌激光器系统的同步

利用反馈控制和分数阶系统稳定性理论,实现了分数阶混沌激光器混沌系统的混沌同步,给出了反馈控制器的具体形式和同步理论的严格数学证明.在同步过程中并未删去响应系统的任何非线性信息,数值仿真结果和理论分析结果的一致性表明了该方法的有效性.     

分数阶混沌系统的DSP Builder设计方法

为了克服模拟电路分数阶混沌系统设计易受外界条件影响,提出了一种基于DSP Builder设计分数阶混沌系统的方法.以分数阶Jerk系统为例,采用一种数字差分算法设计混沌系统,分析了分数阶混沌系统的动力学特性.仿真结果表明,分数阶混沌系统的DSP Builder设计方法是一种有效的分析方法,这为分数阶混沌系统的数字设计提供了新的思路.     

基于分数阶统一混沌系统的图像加密

文章分析了由三种典型混沌系统,即Lorenz系统、Chen系统和系统,统一实现的一种新的分数阶混沌系统,然后利用该混沌系统产生的混沌序列对一幅图像分别进行了像素位置置乱和图像的灰度值替代。仿真实验结果表明,该算法具有良好的像素值混淆、扩散性能,并且能够抵抗穷举搜索攻击、统计分析攻击和已知明文攻击,抗噪声性能也表现良好。     

分数阶Lorenz系统状态反馈控制

引入了分数阶Lorenz混沌系统及分数阶系统稳定的充分条件, 给出了分数阶Lorenz系统的状态反馈控制方法并对受控系统进行了稳定性分析.仿真实验验证了该方法能有效地控制混沌系统到失衡的平衡点.     

新的分数阶混沌系统及其同步控制

研究了一个新的分数阶系统的混沌动力学行为.基于分数阶微积分理论和数值模拟,发现在该新的分数阶系统中存在混沌,并且得出该分数阶系统能产生混沌吸引子的最低阶数为2.49阶.根据分数阶动力系统稳定性理论,通过设计非线性控制器,实现了新的分数阶混沌系统的投影同步,该方法设计简便,并且不需要计算Lyapunov指数,数值模拟结果验证了该同步方法的有效性.     

分数阶Unscented卡尔曼滤波器研究

分数阶微积分在控制系统中的应用日益广泛,随着分数阶动态系统模型的引入,需要求解分数阶状态估计问题的方法。该文从分数阶非线性动态系统模型出发,以概率论为基础,导出分数阶的Unscented卡尔曼滤波器,得到其递推模型并应用于典型的非线性系统,UNGM(Univariate Nonstationary Growth Model)模型和再入飞行器跟踪模型。实验结果证明在合理设置分数阶Unscented 卡尔曼滤波器阶次的情况下,能够取得优于Unscented 卡尔曼滤波器的效果。     

变参数细胞神经网络的分数阶可切换多元电路设计及仿真

构建新的整数阶三维细胞神经网络系统,通过对其非线性动力学分析、数值计算与电路仿真,验证了该系统混沌吸引子的存在性及物理上的可实现性。同时通过调节线性参数b,研究了新的细胞神经网络系统在基于分数阶qi（i＝1,2,3）不同组合条件下所表现出的混沌特性。结合分数阶电路理论分析分数阶电路中各单元电路形式,并设计了相应参数b可变、阶数值qi可切换的分数阶细胞神经网络电路系统。经统计本设计可实现13824种多元组合电路,并选取具有代表性组合电路进行电路仿真。仿真结果表明,多元电路仿真和数值仿真具有相似的混沌相图,从而证实了细胞神经网络在分数阶条件下仍表现出丰富的动力学特性,具有灵活实用价值和现实推广意义。     

Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach

In this paper, a board class of uncertain fractional-order nonlinear systems is considered. A novel fractional-order sliding mode controller for output tracking of a time-varying reference signal is designed which can conquer the uncertainties and guarantees the asymptotic convergence of the system output toward the desired time-varying reference signal. For this purpose, an appropriate sliding surface is designed where maintaining the system’s states on this surface leads to asymptotic vanishing of error signal. Moreover, by tacking the fractional derivative of order α from the sliding surface, the convergence of system’s trajectories into the sliding surface in a finite time is proven. Finally, in order to verify the theoretical results, the proposed method is applied to a fractional-order gyroscope model and computer simulations show the efficiency of the proposed method in output tracking.     

A simple fractional-order chaotic system without equilibrium and its synchronization

There has been an increasing interest in discovering no-equilibrium chaotic systems recently. In this paper, a novel three dimensional fractional-order chaotic system, which has no equilibrium, is introduced. Dynamics of the system has been studied. It is interesting that the system can exhibit coexisting chaotic attractors for the order as low as 2.7. The adjustable feature of a variable is studied by introducing a single controlled constant. Circuit implementation of the system is proposed to show its feasibility. In addition, we have designed the controllers to investigate coexisting synchronization types of such a new fractional-order system. Numerical examples have verified the proposed synchronization schemes.     

Coexistence of infinite attractors in a fractional-order chaotic system with two nonlinear functions and its DSP implementation

In this paper, a new five-dimensional fractional-order chaotic system based on two nonlinear functions is constructed. The rich dynamical behaviors of the system are analyzed by phase diagram, bifurcation diagram and Lyapunov exponents spectrum. In addition, the complexity of the fractional-order system is analyzed through Spectral Entropy (SE) and Permutation Entropy (PE) algorithms. Meanwhile the phenomenon of coexisting infinite attractors is analyzed. Of particular concern is that the phenomenon of multi-state transition and intermittent oscillation chaos is found in this new chaotic system. Furthermore, the system is implemented on the DSP platform. To the best of the knowledge, these rich dynamical characteristics and complicated phenomena are of great reference value in chaotic image encryption and other fields.     

Creep modeling and identification for piezoelectric actuators based on fractional-order system

This paper deals with creep modeling and identification for the piezoelectric actuator (PEA). Creep is an essential phenomenon when a PEA operates over long periods of time. A fractional-order model is proposed by representing the PEA as resistocaptance, which is a novel approach. The simplified fractional-order PEA model results in a double-logarithmic creep. Identification methods for PEA parameters are presented. Experimental results validate the effectiveness of the proposed fractional-order creep model.     

A new S-box construction method based on the fractional-order chaotic Chen system

Since substitution box (S-box) is the only nonlinear component related to confusion properties for many block encryption algorithms, it is a necessity for the strong block encryption algorithms. S-box is a vital component in cryptography due to having the effect on the security of entire system. Therefore, alternative S-box construction techniques have been proposed in many researches. In this study, a new S-box construction method based on fractional-order (FO) chaotic Chen system is presented. In order to achieve that goal, numerical results of the FO chaotic Chen system for \(a= 35, b=3, c=28\) and \(\alpha =0.9\) are obtained by employing the predictor–corrector scheme. Besides, a simpler algorithm is suggested for the construction of S-box via time response of the FO chaotic Chen system. The performance of suggested S-box design is compared with other S-box designs developed by chaotic systems, and it is observed that this method provides a stronger S-box design.     

Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems

This paper concerns with the problem of designing a passivity-based fractional-order (FO) integral sliding mode controller for uncertain FO nonlinear systems. Utilizing the FO calculus, it is showed that the state trajectories of the closed-loop system reach the FO switching manifold in finite time. The control law ensures the asymptotical stability on the sliding surface. A parameter adjustment scheme for FO integral sliding surface is proposed by using the linear matrix inequality (LMI) approach. The proposed controller can be applied to different systems such as chaotic systems. Finally, simulation results are provided to show the effectiveness of the proposed method controlling chaos in FO Chua circuit and FO Van-der-Pol oscillator.     

Simulation of a proposed near-field-to-far-field antenna measurement system

A new antenna-pattern measurement method for antennas with large far-field distances is proposed. The method is applicable to conventional antenna ranges with two axis mounts and with pattern recording in amplitude only, It requires only a few minor items of additional equipment. A computer simulation has been carried out and the results are presented.     

一个混沌系统仿真研究及其电路分析

分析了Liu混沌系统动力学特性,首先对系统的数值特性进行了分析和研究。通过数值分析可以得到系统是混沌的。给出了MultiSim10.1软件实验系统的拓扑结构,并进行了硬件电路的设计和电路仿真研究。电脑仿真技术为研究非线性系统提供了可行的方案,此实验系统具有良好的实验效果,与传统的自治混沌系统相比,此系统具有参数调节方便、易实现、可靠性高,实时性好等优点。     

Capacitorless digitally programmable fractional-order filters

Novel topologies of fractional-order filters, implemented using the internal gate-source capacitance of MOS transistors, are introduced in this paper. This has been achieved using current-mirrors as active elements, resulting into resistorless realizations due to the employment of the small-signal transconductance parameter of the MOS transistor. This also offers the capability for electronic tuning of the frequency characteristics of the derived filter structures. The evaluation of the proposed technique has been performed through the design of a generalized fractional-order filter, which is also digitally programmed in such way that the four standard filter functions are offered. The behavior of the filter has been evaluated using the Cadence IC design suite and the Design Kit provided by the Austrian Micro Systems 0.35 μm CMOS process.     

Passivity-based non-fragile control of a class of uncertain fractional-order nonlinear systems

This article investigates the issues of passivity and feedback passification of a class of fractional-order (FO) nonlinear systems with time-varying norm-bounded parameter uncertainties in both the state and output matrices. Firstly, new passivity conditions presented by linear matrix inequalities (LMIs) are established based on new notions of passivity of FO systems. Secondly, considering inaccuracies or uncertainties may occur during controller implementation, non-fragile state feedback passification controller is proposed when the states are available. The obtained results extend and improve some recent results. Finally, the applicability and effectiveness of the developed results are examined via numerical examples with simulation results.