分数阶超混沌Lorenz系统的数值求解及其动力学特性分析

采用预估-校正算法和Adomian分解算法求解分数阶超混沌Lorenz系统,并对比研究两种算法结果。从得到的吸引子和频谱结果来看,两种算法得到的结果比较一致,都可用于分数阶混沌系统数值求解。分析了系统的动力学特性和C0复杂度,实验结果表明分数阶Lorenz系统具有丰富的动力学特性,采用Adomian算法能够得到更小的系统产生混沌最小阶数,当参数变化时,系统的混沌范围更广。最后基于C0复杂度设计了一种有效的系统参数选取算法。为分数阶混沌系统应用提供了理论与实验基础。     

Fractional-Order Control for a Novel Chaotic System Without Equilibrium

The control problem is discussed for a chaotic system without equilibrium in this paper. On the basis of the linear mathematical model of the two-wheeled self-balancing robot, a novel chaotic system which has no equilibrium is proposed. The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincaré map. To further demonstrate the physical realizability of the presented novel chaotic system, a chaotic circuit is designed. By using fractional-order operators, a controller is designed based on the state-feedback method. According to the Gronwall inequality, Laplace transform and Mittag-Leffler function, a new control scheme is explored for the whole closed-loop system. Under the developed control scheme, the state variables of the closed-loop system are controlled to stabilize them to zero. Finally, the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.      

Robust Fractional-Order Proportional-Integral Observer for Synchronization of Chaotic Fractional-Order Systems

In this paper, we propose a robust fractional-order proportional-integral (FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional (FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.      

Delay-dependent consensus condition for a class of fractional-order linear multi-agent systems with input time-delay

The consensus problem of a class of fractional-order linear multi-agent systems with distributed control containing input time-delay is investigated. By adopting the frequency domain analysis and generalised Nyquist criterion for the fractional-order time-delay systems, the delay-dependent consensus condition is obtained. Then, we are interested in finding the maximum time-delay tolerance and give an exact formula for calculating the maximum time-delay to maintain the system is consensusable. As illustrated by the numerical examples, the proposed theoretical results work effectively and accurately.     

分数阶复杂网络的混合投影同步研究

主要针对一类节点为分数阶混沌系统的复杂网络混合投影同步进行研究.基于分数阶系统的稳定性理论和非线性反馈控制方法,通过设计有效的控制器,实现了不同节点的复杂网络的混合投影同步,并给出了实现投影同步的充分条件,不仅从理论上分析了该控制器可以使复杂网络系统实现投影同步,而且大量的数值模拟证明所设计控制器的正确性和有效性.     

Optimal Tuning of FOPID-Like Fuzzy Controller for High-Performance Fractional-Order Systems

This paper addresses improvements in fractional order (FO) system performance. Although the classical proportional–integral–derivative (PID)-like fuzzy controller can provide adequate results for both transient and steady-state responses in both linear and nonlinear systems, the FOPID fuzzy controller has been proven to provide better results. This high performance was obtained thanks to the combinative benefits of FO and fuzzy-logic techniques. This paper describes how the optimal gains and FO parameters of the FOPID controller were obtained by the use of a modern optimizer, social spider optimization, in order to improve the response of fractional dynamical systems. This group of systems had usually produced multimodal error surfaces/functions that occasionally had many variant local minima. The integral time of absolute error (ITAE) used in this study was the error function. The results showed that the strategy adopted produced superior performance regarding the lowest ITAE value. It reached a value of 88.22 while the best value obtained in previous work was 98.87. A further comparison between the current work and previous studies concerning transient-analysis factors of the model’s response showed that the strategy proposed was the only one that was able to produce fast rise time, low-percentage overshoot, and very small steady-state error. However, the other strategies were good for one factor, but not for the others.     

基于分数阶模式的高拱坝变形安全监控研究构想

为科学监控服役过程中高拱坝的变形安全,基于高拱坝结构特性和服役特点,在分析分数阶元件模型、混凝土坝物理力学参数反演、混凝土坝变形安全监控发展动态的基础上,依据分数阶建模理论,提出了一种高拱坝变形安全监控研究思路与构想:围绕高拱坝变形性态分数阶数值模拟以及基于分数阶模式的单测点和测点群变形安全监控这两个互相关联的科学问题,沿着“分数阶元件模型→物理力学参数反演→单测点变形安全监控→测点群变形安全监控”的研究主线,遵循“基础到深入、简单到复杂、现象到本质、理论到应用、局部到整体、一维到多维” 的原则开展研究。为实现研究构想,重点需攻克三维高应力状态下高拱坝加速流变效应分数阶元件模型、分数阶元件模型弹性和黏弹性物理力学参数反演,以及高拱坝时效变形分数阶分析模型这3个关键的科学技术问题。     

基于分数阶阻抗模型的磷酸铁锂电池荷电状态估计

锂电池荷电状态(SOC)估计是电池管理系统中不可或缺的重要组成部分。锂电池传统整数阶等效电路模型未充分考虑其内部电化学反应现象,故将导致SOC估计结果偏离真实状态。文中以磷酸铁锂电池单体为研究对象,提出一种基于分数阶阻抗模型的锂电池SOC估计方法。该方法利用分数阶元件表征锂电池内部固液界面的输运现象和极化效应,基于分数阶微分理论建立状态转移方程和系统量测方程,并针对锂电池高度非线性的工作特性,利用无迹变换逼近原始状态分布,运用分数阶无迹卡尔曼滤波算法估计锂电池SOC。实验结果表明,分数阶阻抗模型能准确描述锂电池工作特性,所提算法在估计精度和跟踪速度上有一定提高。