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.     

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。     

基于分数阶忆容器的有源滤波器设计

在分析研究整数阶忆容器模型和分数阶忆容器模型的基础上,提出了一种具有两个分数阶阶次的忆容器模型,并对其相关特性进行了分析。将此模型应用于有源低通滤波电路中,仿真分析了含有分数阶忆容器的有源低通滤波电路的时域和频域特性。实验结果表明,与整数阶忆容器模型相比,提出的分数阶忆容器模型可以通过改变分数阶阶次来调整低通滤波电路的截止频率,进而改变低通滤波电路的滤波效果。     

六维分数阶Lorenz-duffing系统仿真

设计一个混沌行为复杂且具有物理学特性的整数阶混沌系统很难。为了解决这个问题,在整数阶混沌系统中引入了分数阶微分算子,并设计了一个六维分数阶Lorenz-duffing混沌系统;还重点分析了该分数阶混沌系统的平衡点和稳定性以及系统的吸引子、分岔图和Lyapunov指数谱;最后,设计该分数阶混沌电路,并利用Multisim软件仿真分析了该电路。仿真结果表明,该分数阶混沌系统能够产生混沌信号。     

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.     

电容的分数阶等效电路建模与分析

实际的电容器件都是非理想的,其特性受到各种因素的影响,建立精确的电容模型对于电路系统分析与设计十分必要。考虑到电容的分数阶微积分特性,文中基于传统的电容整数阶等效电路模型,提出电容的分数阶等效电路模型,并采用差分进化算法辨识出模型参数,然后将该模型应用于Buck电路进行纹波电压的分析。仿真结果表明,同传统整数阶等效电路模型相比,分数阶等效电路模型拟合电容实际数据的准确度更高,验证了该电容分数阶等效电路模型的有效性。     

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。     

基于分数阶微分的图像增强算法

相比传统的基于整数阶微分的图像增强算子,分数阶微分增强算子能提升图像的高频边缘信息,且非线性保留图像纹理细节和平滑区域的中低频信息。文中根据Riemann-Liouville分数阶微分定义,构造了5×5大小的分数阶微分增强算子模板,同时采用传统的整数阶图像增强算子Sobel算子、Prewitt算子和Laplacian算子,分别对灰度图像和彩色图像进行图像增强处理实验。最后,引入图像熵的计算,对图像增强的结果进行熵值大小的计算与分析。随着分数阶微分阶次的增加,分数阶微分增强算子处理后的图像熵值呈上升趋势,说明图像的纹理细节信息得到了加强。     

异结构的分数阶超混沌系统函数投影同步及参数辨识

该文以分数阶Chen混沌系统和一个新的分数阶超混沌系统为例,研究参数不确定的分数阶混沌系统和超混沌系统函数投影同步及参数辨识。首先,基于分数阶系统稳定性理论和非线性动力学理论,构造出相应的非线性控制器和不确定参数的辨识规则;由此实现了参数不确定的分数阶超混沌系统的函数投影同步及不确定参数的辨识。其次,利用分数阶稳定性理论,对上述同步给出了严格的数学证明。最后,借助于预估-校正算法,利用数值模拟验证了所提方法的有效性。     

一种基于分数阶的电池荷电状态估计方法

本文首先简单介绍了分数阶微分的相关知识,以及分数阶系统的优点,然后在整数阶模型的基础上,将整数阶中的元件用分数阶的相关元件替代,建立出分数阶模型,最后使用改进的双扩展卡尔曼滤波和双卡尔曼滤波这两种算法来对电池SOC进行估算,利用仿真软件对两种算法的结果做对比,得到一种估算精确度比较高的算法。     

基于投影法的不确定分数阶混沌系统自适应同步

针对一类具有未知参数、未知非线性函数及外部扰动的分数阶混沌系统,基于分数阶系统稳定性理论和Lyapunov稳定性理论,该文提出一种基于滑模自适应和投影法的同步控制策略。首先选取一类稳定的分数阶积分滑模面,运用自适应技术对不确定项进行估计,设计了同步控制器。然后对自适应设计中容易出现的增长型自适应律运用投影法进行修正,以保证参数有界,从而也保证控制输入有界。最后数值仿真证明了所设计控制器的正确性和有效性。     

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.     

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.     

Arbitrary real-order cost functions for signals and systems

This work focuses on a new type of cost function based on fractional operators. To do so, the concept of definite integral is extended to arbitrary real-order. Some properties of this new fractional-order definite integral are studied and a fractional-order Barrow's rule is proposed. It is illustrated by an example (the design of an IIR filter) how this new kind of cost function can be a valuable tool in problems where optimal design methods are involved.     

分数阶微积分的一种物理解释和定域长分数阶微积分

本文讨论了现有的三种分数阶微积分基本定义(R-L(Riemann-Liouville)定义、G-L(Grumwald-Letnkov)定义和Caputo定义)对阶数的适用范围,以及三者之间的关系;强调指出分数阶导数与整数阶导数之间的区别.通过对分数阶微积分一个统一公式的讨论,以及给出分数阶微积分一个简单的物理解释,加深对分数阶微积分本质的认识;提出定域长分数阶微积分定义,给出它的直接数值算法,预期它可能在实践中得到应用.     

A New Fractional-Order Chaotic System and Its Synchronization with Circuit Simulation

A new fractional-order chaotic system is proposed in this paper, and a list of state trajectories is presented with fractional derivative of different areas. Furthermore, a circuit diagram is studied to realize the fractional-order chaotic system. The new fractional-order chaotic system can be controlled to reach synchronization based on the nonlinear control theory, and the results between numerical emulation and circuit simulation are in agreement with each other.     

外部光注入分布反馈激光器的非线性动力学特性

实验研究了外部光注入分布反馈(DFB)激光器的非线性动力学行为,并给出了其输出特性随注入光强度和频率失谐量变化的动力学特征图.实验结果表明,激光器的动力学行为对外部的微扰十分敏感;在不同外部光注入条件下,激光器可以呈现出单周期、倍周期、多周期以及混沌等多种非线性动力学特征;在注入光强度和频率失谐量变化空间存在三个复杂动力学区域;激光器表现出的复杂动力学行为总是与周期行为有关;当激光器处于复杂动力学区域时,其频谱为连续谱,在连续谱上存在多个明显的峰,所对应的频率定义为特征频率,特征频率的大小不随注入光的强弱以及频率变化.     

Auto-tuning of PID controller according to fractional-order reference model approximation for DC rotor control

This paper presents a stochastic, multi-parameters, divergence optimization method for the auto-tuning of proportional–integral–derivative (PID) controllers according to a fractional-order reference model. The study aimed to approximate the step response of the real closed-loop flight control system to the response of a theoretical reference model for a smoother and more precise flight control experience. The proposed heuristic optimization method can auto-tune a PID controller without a precise plant model. This is very advantageous when dealing with model and parameter uncertainties in real control application and practice. Experimental study confirms the reference model driven auto-tuning of the DC rotor prototype.     

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.