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

This article focuses on the consensus problem of leader-following fractional-order multi-agent systems (MASs) with general linear and Lipschitz nonlinear dynamics. First, the distributed adaptive protocols for linear and nonlinear fractional-order MASs are constructed, respectively. We allow the control coupling gains to be time varying for each agent. Moreover, the adaptive modification schemes for the control gain are designed, which renders smaller control gains and thus requires smaller amplitude on the control input without sacrificing consensus convergence. Second, based on fractional-order Lyapunov stability theorem and Barbalat's lemma, two novel sufficient conditions in terms of linear matrix inequalities are provided to ensure that the leader-following consensus can be obtained in the case for any undirected connected communication graph. Furthermore, we show that the proposed algorithm also works for consensus of agents with intrinsic Lipschitz nonlinear dynamics. As a result, the proposed framework requires no global information and thus can be implemented in a fully distributed manner. Finally, the numerical simulations are given to demonstrate the effectiveness of obtained the theoretical results.     

Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays

In this paper, we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time-varying communication delays. By employing a linear matrix inequality method, we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected. Particularly, several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying communication delays. Numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results.     

Input-output finite-time stability of time-varying linear singular systems

This paper studies the input-output finite-time stabilization problem for time-varying linear singular systems. The output and the input refer to the controlled output and the disturbance input,respectively.Two classes of disturbance inputs are considered,which belong to L-two and L-infinity.Sufficient conditions are firstly provided which guarantee the input-output finite-time stability.Based on this,state feedback controllers are designed such that the resultant closed-loop systems are input-output finite-time stable.The conditions are presented in terms of differential linear matrix inequalities.Finally,an example is presented to show the validity of the proposed results.     

具有随机丢包的网络化多自主体系统的一致性

研究具有随机丢包的网络化多自主体系统的均方一致性问题,其中不同自主体间的通信通道具有相同的丢包情况并且均服从马尔可夫(Markov)分布。首先,利用系统变换和迭代方法,得到了系统达到均方一致的一个初等充要条件。然后,利用矩阵理论和图论知识,如果拓扑图含有有向生成树,则可以将系统的均方一致性转化成一个线性Markov跳变系统的均方稳定性,并且可以建立线性矩阵不等式形式的均方可镇定准则。最后,通过相应的仿真实例说明了所得结论的可行性。     

计及灵活性储备的含风电多微电网系统分布式协调调控策略

高比例风电的接入和需求响应技术的应用对分布式架构下的多微电网系统有功功率动态平衡提出了更高的要求,有必要充分利用灵活性资源对系统进行协调调控.提出一种新颖的灵活性电池储备模型对多微电网系统灵活性备用容量进行评估,定义虚拟灵活性电池储备模型对风电场备用与需求响应负荷备用进行评估,充分挖掘其调频的潜在能力.在此基础上,基于一致性算法求解该模型下各微电网的功率分配,提出计及灵活性储备的含风电多微电网系统分布式协调调控策略,实现分布式架构下灵活性资源的协调优化.通过华东某地区实际数据验证了所提策略的有效性.算例结果表明,协调优化源-荷灵活性储备资源在保障风电消纳的同时,实现了分布式架构下系统的动态功率平衡.     

Chattering free full-order sliding-mode control

In conventional sliding-mode control systems, the sliding-mode motion is of reduced order. Two main problems hindering the application of the sliding-mode control are the singularity in terminal sliding-mode control systems and the chattering in both the conventional linear sliding-mode and the terminal sliding-mode control systems. This paper proposes a chattering-free full-order terminal-sliding-mode control scheme. Since the derivatives of terms with fractional powers do not appear in the control law, the control singularities are avoided. A continuous control strategy is developed to achieve the chattering free sliding-mode control. During the ideal sliding-mode motion, the systems behave as a desirable full-order dynamics rather than a desirable reduced-order dynamics. A systematic design method of full-order sliding-mode control for nonlinear systems is presented, which allows both the chattering and singularity problems to be resolved. Simulations validate the proposed chattering free full-order sliding-mode control.     

Finite-time coordination in multiagent systems using sliding mode control approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of agents described by fully actuated Euler–Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time. The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network. In addition, we discuss the case of switching communication topologies in multiagent systems. Finally, we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents.     

线性多智能体系统一致性问题的部分稳定性方法（英文）

A linear transformation is proposed to deal with the consensus problem of high-order linear multi-agent systems(LMASs).In virtue of the linear transformation, the consensus problem is equivalently translated into a partial stability problem. We discuss three issues of the LMASs under a generalized linear protocol: 1) to find criteria of consensus convergence; 2) to calculate consensus function; 3) to design gain matrices in the linear consensus protocol. Precisely, we provide a necessary and sufficient criterion of consensus convergence in terms of Hurwitz stability of a matrix and give an analytical expression of the consensus function. In addition, we set up a relation between the gain matrices in the protocol and the convergence time and consensus accuracy of the agents, and then design the gain matrices with respect to a pre-specified convergence time and a required consensus accuracy.     

Non-existence of finite-time stable equilibria in fractional-order nonlinear systems

We note that in the literature it is often taken for granted that for fractional-order system without delays, whenever the system trajectory reaches the equilibrium, it will stay there. In fact, this is the well-known phenomenon of finite-time stability. However, in this paper, we will prove that for fractional-order nonlinear system described by Caputo’s or Riemann–Liouville’s definition, any equilibrium cannot be finite-time stable as long as the continuous solution corresponding to the initial value problem globally exists. In addition, some examples of stability analysis are revisited and linear Lyapunov function is used to prove the asymptotic stability of positive fractional-order nonlinear systems.