The feedback control of fractional order unified chaotic system

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.

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

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.

Stabilizing controller design for nonlinear fractional order systems with time varying delays

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.

Control Chaos in System with Fractional Order

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.

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

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.

Robust Admissibility and Stabilization of Uncertain Singular Fractional-Order Linear Time-Invariant Systems

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.

O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

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.

Chaos in the Fractional Order Logistic Delay System

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.

LMI Based Synchronization Control of Nonlinear Affine Fractional Order Chaotic Systems Considering Input Constraint

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.

Event-Triggered Adaptive Fuzzy Finite Time Control of Fractional-Order Non-Strict Feedback Nonlinear Systems

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.

基于自适应分数阶正位置反馈的垂尾振动主动控制

针对自适应正位置反馈(Adaptive Positive Position Feedback,APPF)控制器在控制效果与分数阶正位置反馈(Fractional Order Positive Position Feedback,FOPPF)控制器在针对摄动区间小的不足,提出一种分数阶APPF(Fractional Order Adaptive Positive Position Feedback,FOAPPF)控制器,使得控制器在控制效果提升的同时兼具强鲁棒性。基于不同参数对FOPPF控制器的影响,推导参数的最佳范围,将系统多个摄动模型的正弦扫频响应进行综合加权处理,并考虑系统远离共振频段的控制性能,构建附带约束条件的控制设计的目标函数。以粘有宏纤维复合材料(Macro Fiber Composites,MFC)的垂尾模型及其摄动模型为被控对象,设计相应的FOAPPF控制器。研究结果表明:相比FOPPF控制器,FOAPPF控制器闭环极点对参数摄动不敏感;相比APPF控制器,FOAPPF控制器的相频曲线在摄动频带内变化平缓,其控制效果受固有频率在线估计误差的影响更小;多种试验工况表明,FOAPPF控制器在不同摄动模型下均具有较好的控制效果,垂尾抖振响应均方根值至少降低了55%,且具有较好的鲁棒性,因此该控制器对垂尾结构的振动主动控制具有良好应用潜力。

无刷直流电机短反馈分数阶PID滑模的优化控制

针对无刷直流电机(BLDCM)的非线性、强耦合、多变量及参数时变等特性,导致其调速系统的控制性能欠佳的问题,提出了一种灰色预测短反馈分数阶PID滑模优化控制算法。引入内分泌激素调节中的超短反馈算法构成系统双层反馈机制,补偿自身的输出信号;系统反馈环节,引入GM(1,1)模型灰色预测,用灰色预测值取代测量值进行超前控制运算。针对分数阶PID型滑模趋近律参数,采用了一种改进蜣螂优化算法进行寻优,实现更加精确的控制。仿真模拟对比实验结果表明,经蜣螂算法优化的灰色预测短反馈分数阶PID滑模控制下的无刷直流电机调速控制系统,具有比常规PID控制更出色的响应速度、控制精度和鲁棒性等性能。

Comparative study on bifurcation control methods in a fractional-order delayed predator-prey system

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.

基于闭环辨识模型的永磁同步直线电机分数阶反馈控制方法

为了提高永磁同步直线电机(PMLSM)的跟随精度,提出了一种基于闭环辨识模型的分数阶反馈控制方法,通过对反馈控制系统误差幅值特性进行特定分数阶次形式的精准调节来有效抑制PMLSM的跟随误差。该方法推导了PMLSM闭环辨识模型,通过误差幅值特性分析,确定了分数阶超前-滞后补偿器参数选定方法,以实现分数阶反馈控制系统对PMLSM控制频域特性的准确描述,进而提高PMLSM辨识精度及控制性能。采用所提方法在PMLSM龙门运动平台上进行辨识方法和不同运动规划的跟踪实验及圆轨迹运动实验的验证,实验结果表明,该闭环辨识方法能有效抑制外界对辨识信号的干扰,所建立的闭环辨识模型准确性高;相较于PID控制方法,所提分数阶反馈控制方法能够大幅减小PMLSM跟随误差,对于不同运动规划,跟随误差的均方根误差值减小至少82.47%,验证了所提方法可有效提高PMLSM跟踪精度。

具有时滞反馈控制的分数阶HR神经元模型的动力学分析

本文研究了具有时滞反馈控制的分数阶Hindmarsh-Rose(HR)神经元模型的动力学性质.利用稳定性理论和分岔分析方法,详细研究了分数阶阶数和时滞对系统平衡点稳定性、分岔和放电行为的影响.同时获得了在分数阶模型中产生Hopf分岔的解析条件,推广了具有时滞反馈控制的整数阶HR神经元模型的相关结果.

磁悬浮平台直线同步电动机悬浮系统的分数阶反步控制

为了提高磁悬浮平台直线同步电动机悬浮系统的性能,提出了一种分数阶反步控制策略。基于磁悬浮直线同步电动机(MLLSM)悬浮系统的运行机理,建立了其数学模型和状态空间方程;针对MLLSM悬浮系统的强非线性,通过非线性坐标映射对其进行输入输出反馈线性化处理;引入了分数阶理论构造分数阶虚拟稳定函数来提高系统的收敛速度和控制精度;设计了分数阶反步控制器,构造Lyapunov函数证明系统稳定性。仿真结果表明,分数阶反步控制能够提高悬浮系统响应速度,有效抑制不确定性扰动对悬浮系统的影响。

具有时滞的分数阶忆阻神经网络固定时间同步

文中研究了分数阶忆阻神经网络的固定时间同步问题。根据忆阻器的电压电流特性,建立一类具有时变时滞的分数阶忆阻神经网络模型。与传统的基于最大绝对值的记忆突触权值计算方法不同,通过引入数学变换,利用微分包含理论和集值映射,在Filippov解的框架下将分数阶忆阻神经网络转化为一类具有不确定参数的分数阶系统。在固定时间稳定性理论和可测选择定理的基础上,通过构造Lyapunov函数和利用不等式技术给出其固定时间同步的充分条件,并给出同步时间上界的计算式。通过反馈控制方法,构造合适的状态反馈控制器,使主从系统实现固定时间同步,且同步时间的上界与系统初始状态无关。通过仿真算例可看出所设计的控制器可以使系统快速地实现同步。

基于输出反馈滑模控制的分数阶超混沌系统同步

以具有更大秘钥空间的分数阶超混沌系统为驱动系统和响应系统,利用具有实际应用意义的输出反馈滑模控制实现两个系统的同步.通过对同步误差系统方程进行结构分解,在辅助系统的基础上设计具有输出反馈特性的滑模控制律.在分数阶系统稳定性理论基础上利用MATLAB YALMIP工具箱对滑模参数进行整定,并利用分数阶Lyapunov稳定性定理证明了滑模控制律和自适应滑模控制律的稳定性.最后,数值仿真表明了本文方法的有效性和可行性.

分数阶混沌金融模型的时滞反馈控制策略

该文研究了一类分数阶金融模型的混沌控制问题.运用时滞反馈控制法成功控制了金融模型的混沌行为,建立了该模型平衡点稳定及Hopf分支存在的充分条件,揭示了时滞和分数阶的阶数对该模型的稳定性和分支的影响.计算机模拟验证了理论分析的正确性,研究结果为维持金融稳定提供了理论依据.

分数阶L系统中的混沌及其控制

研究了分数阶L系统的混沌动力学行为、数值腄庵っ鞣质譒系统存在混沌,并且得出分数阶L系统能产生混沌吸引子的最低阶数为2.5阶。利用线性反馈控制法研究了分数阶L混沌系统的混沌控制问题,得出了受控分数阶L混沌系统的混沌轨道达到不稳定平衡点时的条件,数值模拟进一步验证了该方法的有效性。