具有时滞及随机特性的复杂动态网络同步问题研究

发布时间：2018-05-25 15:31

本文选题：复杂动态网络 + 同步　；参考：《哈尔滨工业大学》2015年博士论文

【摘要】：近年来,由于在理论领域的重要意义以及在工程领域的广泛应用,复杂动态网络成为了一个热门的研究领域。总体而言,复杂动态网络由许多个动态节点组成,这些节点按照一定拓扑结构进行信息交换从而展示出群体特性。复杂动态网络在现实世界中的典型应用包括因特网、生物神经网络、电力网络、社交网络等。同步问题作为复杂动态网络中的一个基础性问题受到了研究学者越来越多的重视。需要指出的是,时滞现象广泛存在于复杂动态网络中,包括单个节点内部的时滞特性以及节点之间通信存在的信息交换延迟。众所周知,时滞的存在将可能降低复杂动态网络的同步性能甚至破坏复杂动态网络的同步。因此,时滞现象应该在复杂动态网络的同步问题中被考虑。此外,复杂动态网络还常常展示出一定的随机特性,这些特性包括随机非线性、随机时滞、随机参数不确定性等。这些随机特性的引入将进一步完善复杂动态网络模型的描述。考虑到上述问题,本文重点研究了具有时滞及随机特性的复杂动态网络的同步问题,主要研究工作可以总结为以下几个方面:针对存在外部扰动与时变时滞的复杂动态网络,在驱动-响应框架下研究了混合H_∞与无源性指标下的复杂动态网络同步问题。在混合H_∞与无源性指标的基础上,通过构造Lyapunov-Krasovskii泛函建立了时滞依赖的充分性条件从而确保驱动网络可以同步响应网络。仿真结果表明了所设计控制方案的有效性与适用性。在驱动-响应框架下,由于同步控制器在实际应用中往往难以精确的按照设计参数实施,研究了带有随机非线性以及随机控制器增益波动的复杂动态网络同步问题。此外,模型还考虑了节点中存在的时变时滞现象。通过引入随机变量描述随机现象,构造了一组非脆弱同步控制器用于解决同步问题。利用随机分析得到了实现同步的时滞依赖充分性条件。通过一个数值仿真例子证明了所得到的理论结果的正确性。进一步研究了扰动环境下的复杂动态网络的驱动-响应H_∞非脆弱同步问题。特别地,在复杂动态网络的模型中考虑了随机参数不确定性以及随机控制器增益波动对于同步性能的影响,从而更好的反应现实世界中复杂网络的动态特性。建立了实现满足所设定的H_∞同步性能指标的充分性条件。在所得到结果的基础上,进一步设计了一组同步控制器从而实现扰动环境下的同步。给出了一个解释性的例子,仿真结果表明所设计的控制器可以实现给定H_∞指标下的同步。此外,针对复杂动态网络节点间信息传输过程中存在的时滞问题,研究了带有随机时变信息传输时滞的非脆弱受控自同步问题。其中,节点的模型为非线性有利于更好的描述网络的动态特性。此外,控制器中的增益波动也被描述为随机发生的。通过利用Lyapunov-Krasovskii泛函方法得到了时滞依赖的同步准则。进一步地,根据得到的同步条件设计了一组非脆弱控制器从而确保受控自同步可以实现。通过数值仿真的例子证明了所设计的控制方案的有效性与可行性。最后,进一步考虑了控制器存在信息丢失以及外部扰动情况下的复杂动态网络的非脆弱受控耗散自同步问题。需要指出的是,由于实际应用中信息丢失的发生往往是随机的,因此采用随机模型来描述同步控制器存在的随机信息丢失。此外,讨论了复杂动态网络中的时变随机耦合时滞对于同步性能的影响。通过引入耗散性同步指标,建立了相应的时滞依赖充分性条件。在此基础上设计了一组控制器来确保受控同步的实现。相应的给出了一个解释性的例子,仿真结果表明了所得到理论结果的正确性与有效性。
[Abstract]:In recent years, complex dynamic networks have become a hot research field because of their importance in the field of theory and in the field of engineering. In general, complex dynamic networks are composed of many dynamic nodes. These nodes display group characteristics according to a certain topology. Complex dynamic networks. The typical applications of the collaterals in the real world include the Internet, the biological neural network, the power network, the social network and so on. As a fundamental problem in the complex dynamic network, the synchronization problem has been paid more and more attention by the researchers. It is necessary to point out that the time-delay phenomenon is widely stored in the complex dynamic network, including the internal of a single node. It is well known that the existence of time delay may reduce the synchronization performance of complex dynamic networks and even destroy the synchronization of complex dynamic networks. Therefore, time delay should be considered in the synchronization of complex dynamic networks. In addition, complex dynamic networks are often shown. These characteristics include random nonlinear, random time delay, random parameter uncertainty, etc. the introduction of these random properties will further improve the description of the complex dynamic network model. Considering the above problems, this paper focuses on the synchronization problems of complex dynamic networks with time delay and randomness. The work can be summed up in the following aspects: for complex dynamic networks with external disturbances and time-varying delays, the complex dynamic network synchronization problem under the hybrid H_ infinity and passivity index is studied under the drive response framework. On the basis of the mixed H_ infinity and passivity index, the time delay is established through the construction of the Lyapunov-Krasovskii functional. The simulation results show the effectiveness and applicability of the designed control scheme. In the drive response framework, the synchronization controller is often difficult to implement accurately according to the design parameters in the practical application, and studies the random nonlinear and random control. In addition, the model also takes into account the time-varying time-delay phenomena in the nodes. By introducing random variables to describe random phenomena, a group of non fragile synchronization controllers are constructed to solve synchronization problems. The time delay dependence sufficiency conditions for synchronization are obtained by random analysis. An example of numerical simulation proves the correctness of the theoretical results. The driving response H_ infinity synchronization problem of complex dynamic networks under disturbance environment is further studied. In particular, the uncertainty of random parameters and the effect of random controller gain fluctuation on synchronization performance are considered in the model of complex dynamic networks. In order to respond better to the dynamic characteristics of the complex network in the real world, a sufficient condition to meet the set of H_ infinity synchronization performance indicators is established. On the basis of the results obtained, a set of synchronization controllers are designed to achieve synchronization in the disturbance environment. An explanatory example is given and the simulation result table is given. The controller designed by Ming can realize the synchronization under given H_ infinity. In addition, the non fragile controlled self synchronization problem with random time-varying information transmission delay is studied for the time delay problem in the process of information transmission between nodes in complex dynamic networks. The model of the node is nonlinear, which is beneficial to describe the network movement better. Furthermore, the gain fluctuation in the controller is also described as a random occurrence. By using the Lyapunov-Krasovskii functional method, a synchronization criterion for time delay dependence is obtained. Further, a set of non fragile controllers is designed to ensure that the controlled self synchronization can be realized according to the obtained synchronization conditions. An example of numerical simulation is proved. The effectiveness and feasibility of the proposed control scheme is clear. Finally, the non fragile controlled dissipative self synchronization problem of the complex dynamic network under the condition of information loss and external disturbance is further considered. It is necessary to point out that the occurrence of information loss in practical applications is often random, so the random model is used. In addition, the effect of time-varying random coupling time delay on synchronization performance in complex dynamic networks is discussed. By introducing dissipative synchronization index, the corresponding delay dependence sufficiency conditions are established. On this basis, a set of controllers is designed to ensure the realization of controlled synchronization. An explanatory example is given, and the simulation results show the correctness and effectiveness of the theoretical results obtained.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O157.5

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