马尔科夫切换拓扑下带有非一致时变时滞的多智能体系统的H_∞领导跟随一致性问题

研究马尔科夫切换拓扑下带有非一致时变时滞的多智能体系统的H_∞领导跟随一致性问题.通过一个模型变换,把原系统的领导跟随一致性问题转化为新的误差系统的均方稳定性问题.根据马尔科夫时滞系统的稳定性理论,以线性矩阵不等式的形式给出了多智能体系统实现领导跟随一致且具有给定的H_∞性能指标的充分条件.最后,仿真实例验证了理论结果的有效性.     

Bounds on the solution of the time-varying linear matrix differential equation P(t) = AH(t) P(t) + P(t) A(t) + Q(t)

^** Email: pagilla{at}ceat.okstate.edu We derive upper and lower bounds for the trace of the solutionof the time-varying linear matrix differential equation (t)= A^H(t) P(t) + P(t) A(t) + Q(t). A practical numerical exampleis given to verify the bounds. The bounds obtained are usefulsince the considered equation is encountered in a number ofapplications in systems and control theory.     

Modeling and passivity analysis of nonholonomic Hamiltonian systems with rheonomous affine constraints

This paper is devoted to modeling and theoretical analysis of Hamiltonian systems subject to nonholonomic rheonomous affine constraints. We first define rheonomous affine constraints and explain geometric representation of them. Next, a complete nonholonomicity condition for the rheonomous affine constraints is developed in terms of the rheonomous bracket. Then, the nonholonomic Hamiltonian system with rheonomous affine constraints (NHSRAC) is derived via a transformation and model reduction for the expanded Hamiltonian system defined on the expanded phase space. After that, we investigate passivity of the NHSRAC with the control input term and the output equation. Finally, in order to confirm the application potentiality of our new results, we show an example, a radius-variable ball on rotating table with a time-varying angular velocity.     

Synchronization of quaternion-valued coupled systems with time-varying coupling via event-triggered impulsive control

In this paper, the problem of exponential synchronization of quaternion-valued coupled systems based on event-triggered impulsive control is investigated for the first time. It should be pointed out that the coupling strength is quaternion-valued and time-varying, which makes our model more in line with practical models. First, we prove that event-triggered impulsive control can exclude Zeno behavior. Then, based on the Lyapunov method and the graph theory, some sufficient conditions are derived to ensure that quaternion-valued coupled systems reach synchronization. Furthermore, as an application of our theoretical results, exponential synchronization of quaternion-valued Kuramoto oscillators is studied in detail and a synchronization criterion is presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.     

Asymptotic stability of switched linear time-varying systems based on top-floor function

This paper considers the problem of asymptotic stability for switched linear time-varying (SLTV) systems. First, some stability conditions for SLTV systems are given by using infinite integrals. Then, based on the results obtained, two stability conditions are proposed by combining the methods of top-floor function and average dwell time. Moreover, using strict top-floor function, a stability condition is also provided when some subsystems are unstable. With the help of top-floor function, the stability problem of SLTV systems can be simplified and solved by using the technique of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the theoretical results.     

Two classes of time-inhomogeneous Markov chains: Analysis of the periodic case

We consider the M/G/1 and GI/M/1 types of Markov chains for which their one step transitions depend on the times of the transitions. These types of Markov chains are encountered in several stochastic models, including queueing systems, dams, inventory systems, insurance risk models, etc. We show that for the cases when the time parameters are periodic the systems can be analyzed using some extensions of known results in the matrix-analytic methods literature. We have limited our examples to those relating to queueing systems to allow us a focus. An example application of the model to a real life problem is presented.     

多光子J C模型中频率随时间变化场的压缩效应

利用多光子J C模型,考虑场频率随时间以正弦函数形式作小量变化,在旋波近似下,研究了二能级原子通过多光子跃迁与单模辐射场相互作用系统中场的压缩效应.利用数值计算方法讨论了场频率变化的幅值和角频率、以及光场强度对场压缩效应的影响.结果表明：随场频率变化的幅值增大,场压缩效应增强;随光场初始平均光子数的增加,场压缩效应减弱.场正交分量的均方涨落随时间的演化受场频率随时间正弦函数形式变化的调制,场频率变化的幅值越大调制作用越强.     

经济批量排产问题的改进算法:设定最高允许高度

经济批量排产问题是指在生产准备费用与库存费用最低的情况下,协调地、周期性地生产多种产品的问题.由于此问题是NP-hard的,人们一种致力于寻找快速地求解高质量的近似最优解的方法.在将生产次数舍入为2的幂次后,误差小,获得可行解的速度快.研究的经济批量排产问题考虑了产品货架存放期因素.指出了Dobson算法的不足,并提出了基于2的幂次条件的改进算法.改进算法设定了最高允许高度,首先给部分箱进行装箱.由于能获得高质量的生产排产,因此,算法能获得2的幂次条件下的高质量解.给出一个算例,计算结果显示,算法结果更优.     

基于自适应-脉冲控制方法实现时变耦合驱动-响应复杂网络的投影同步

最近,对时变延迟网络的脉冲稳定性的研究大量出现,但通过自适应-脉冲控制方法获得的时变延迟网络同步准则却很少.本文中,运用自适应-脉冲控制方法,设计自适应反馈控制器、自适应律和线性脉冲控制器,研究时变耦合部分线性系统驱动-响应复杂网络的投影同步.获得时变耦合网络的自适应-脉冲投影同步准则.并且不需要网络的耦合构造矩阵是不可约的.另外,运用数值模拟证实方案的有效性和可行性.     

Master-slave synchronization of neural networks with time-varying delays via the event-triggered control

ABSTRACT

This paper investigates the problem of master-slave synchronization of neural networks with time-varying delays via the event-triggered control (ETC). First, the proposed ETC can effectively reduce the total amount of data transmitted to the controller in the synchronization process and avoid communication channel congestion. Second, a master-slave synchronization of neural networks with time-varying delays is constructed, where delays within neural networks and the ETC are simultaneous existence. The controller is updated by the ETC. By the Lyapunov stability theory, some sufficient criteria are obtained to ensure master-slave synchronization of neural networks. Finally, a numerical example and a tunnel diode circuit example are used to verify the validity of results obtained.