Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control

In this paper, the leader-following consensus problem of fractional-order multi-agent systems is considered via adaptive pinning control. The dynamics of leader and all followers with linear and nonlinear functions are investigated, respectively. We assume that the node should be pinned if its in-degree is less than its out-degree in the paper. Under this assumption and based on the stability theory of fractional-order differential systems, some leader-following consensus criteria are derived, which are easily obtained by matrix inequalities. The control of each agent using local information is designed and detailed analysis of the leader-following consensus is presented. The design technique is based on algebraic graph theory and the Riccati inequality. Several simulation examples are presented to demonstrate the effectiveness of the proposed method.     

Stabilisability analysis of high-order unstable processes by fractional-order controllers

In this article, the sufficient stabilisability criteria for unstable time-delay processes by fractional-order controllers are investigated. The process is a high-order system with a single unstable pole, which also has a stable zero. The adopted approach to derive the sufficient conditions for stability is based on the well-known Nyquist stability criterion. Stabilisability is studied by applying fractional-order proportional integral and proportional derivative controllers and the results are given in terms of the maximum allowable value of time delay. Additionally, limitations on the parameters of the controllers which must be taken into account in the controller design are proposed.     

Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay

The distributed formation control of fractional-order multi-agent systems is mainly studied under directed interaction topology in this paper. First, the control algorithm with absolute damping and communication delay is proposed to achieve the formation control. Then, some sufficient conditions are derived by using the matrix theory, graph theory and the frequency-domain analysis method. Finally, based on the numerical method of predictor–corrector, several simulations are presented to illustrate the effectiveness of the obtained results.     

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

This paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.     

含对数项分数阶T混沌系统的滑模同步

利用Barbalat引理、分数阶稳定性理论,通过构造合适的分数阶线性滑模面和分数阶比例积分滑模面,设计合理的控制器,实现整数阶、分数阶T混沌系统滑模同步控制。研究结果表明:一定条件下,分数阶T混沌系统的驱动-响应系统能够达到滑模同步,用Matlab数值仿真验证了结论的正确性。     

分数阶控制系统的空间根轨迹分析法

提出并论证了分数阶控制系统的空间根轨迹分析方法．通过任意阶次引起黎曼面的伸缩得出非整数次方程解的分布与阶次的关系，并由受分数阶影响的主黎曼面构造出分数阶控制系统特征根的运动空间，根据分数阶控制系统根轨迹的相角、幅值条件与阶次条件得到此空间下的系统根轨迹．论述了几何描述与解析2种方法，并给出空间根轨迹与平面根轨迹在主黎曼面意义下的等价关系．     

Stabilization of delayed fractional-order T-S fuzzy systems with input saturations and system uncertainties

By adopting the Takagi–Sugeno (T-S) fuzzy theory, this paper focuses on the adaptive control of fractional-order time-delay systems involving unknown parameters and input saturations. T-S fuzzy systems with “IF-THEN” rules are employed to describe fractional-order nonlinear systems. The influence of input saturation is handled by designing an auxiliary system. By using a norm conversion, the system's time-delay term is converted into a non-delayed form. Adaptive updating rules are devised to evaluate uncertainties of the system, and a new control approach is proposed. The devised controller can not only guarantee the boundedness of variables involved but also make state variables converge into a sufficiently small neighborhood of the origin, even in the presence of uncertainties, saturation functions, and system parameters. Finally, numerical studies are given to verify the correctness of the designed scheme.     

External stability of fractional-order control systems

Stabilityisapreconditionforcontrolsystemsto operatenormally.Anunstablesystemisnotofpracticalvalueinengineering.Thecontrolsystemsusedsofarareallconsideredinteger ordersystems,althoughtherealobjectsaregenerallyfractional[1].Thereasonto disregardtherealorder…     

基于时空分数阶导数模型的潜流带溶质运移模拟

为弥补传统整数阶导数对流-弥散方程在潜流带溶质运移模拟时难以描述介质非均质性引起的溶质运移的不足,在潜流带溶质运移模型中引入时空分数阶导数项,分别从一维和二维角度出发对分数阶导数方法在潜流带溶质运移模拟中的适用性进行讨论。研究发现：时间分数阶阶数α体现溶质运移过程的滞时效应,使穿透曲线具有明显的拖尾特征;空间分数阶阶数β刻画介质非均质性引起的溶质超扩散现象。参数敏感性分析结果表明：引入分数阶方法相较于传统对流-弥散方程使得方程对流速和弥散系数改变的敏感性增强,解决了传统整数阶方法无法准确描述潜流带中介质强非均质性的缺陷。野外示踪试验进一步证明：由于潜流带中介质非均质性强且存在多维流的特点,传统二维整数阶对流扩散方程对溶质运移过程刻画存在不足;一维分数阶导数模型在模拟潜流带溶质运移时,能够更准确计算溶质浓度峰现时间,描述穿透曲线拖尾现象;二维分数阶导数模型受到不同方向参数设置的影响,在没有纵深方向介质差异导致的水流、介质参数差异的前提下,模拟水平面内溶质扩散过程更具适用性。     

基于分数阶微积分的磁流变液粘弹性模拟

建立了磁流变液测试系统的分数阶模型并进行了模拟,在自制的流变仪上针对不同的磁流变液进行了正弦波电流加载验。结果表明:分数阶模型下的计算数据能够较好地拟合试验数据,且磁流变液的粘弹性可由模型参数获得;分数阶系统模型可以从系统角度观察磁流变液的阻尼特性。