复杂动态系统的一致性与耗散性研究
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摘要
过去十来年中,网络的分布式计算主要依靠复杂且昂贵的处理器建立少量但功能强大的工作站来执行任务,近几年,由于计算机技术水平的提高,复杂动态系统迅速发展,基于复杂系统的多智能体网络的优良性质及其广泛的应用前景日益凸显出来。运用简单价廉的智能体之间的协调配合就能完成相同的任务,不仅可以节省成本,而且还提高了整个系统的鲁棒性和灵活性。由于智能体在运行过程中存在能量损耗,因此,复杂动态系统的一致性和耗散性引起了很多专家学者的浓厚兴趣,在世界范围内掀起一股研究复杂动态系统的热潮。
本文以多智能体网络为实际背景,结合控制理论,代数图论以及矩阵论,围绕通讯网络存在的一些问题,如：时滞,噪声,外部干扰等因素,重点研究了基于奇异系统,脉冲系统,以及随机网络环境的一致性问题以及耗散性问题。
由于网络中的智能体不仅接受邻居智能体的信息流而且还受到环境的约束,因此一般情况下多智能体网络可描述为奇异系统。本文在环境约束下研究了基于奇异系统的多智能体网络的一致性问题,研究了在有或无时滞时多智能体网络取得一致性的条件,并研究了在取得一致性的前提下,多智能体网络可以承受的最大时滞,以及收敛到一致性的最差速度,最后研究了固定拓扑和切换拓扑下多智能体网络存在外部干扰和模型不确定性时的鲁棒一致性控制问题。本文研究结果表明,环境约束对多智能体网络取得一致性行为及其性能都有影响,多智能体网络可以承受的最大时滞以及收敛到一致性的速度不仅与多智能体的网络拓扑结构即网络图的拉普拉斯矩阵的特征值有关,而且与环境的约束条件有关。
目前研究一致性的算法基本上都是由连续时间模型或离散时间模型构成的,但是这些模型不能包含现实中一些有用的网络。现实的动态网络可能形成更加复杂的系统,例如切换系统,或更一般的混杂系统。在网络的动态变化过程中,智能体可能受到瞬间的干扰或在某些时刻经历突变,也就是说网络会出现脉冲效应,这些现象在飞行物运动网络,生物网络中广泛存在。在脉冲过程中,智能体可以从与邻居的瞬间接触中获取信息,为了充分利用所获得的信息,本文提出了多智能体网络的脉冲一致性算法,研究了在固定拓扑和切换拓扑结构下多智能体网络取得一致性的条件,一致性的收敛速度,以及抗干扰的能力,并在有时滞的多智能体网络中考虑了相应问题。本文研究结果表明,考虑脉冲信息的一致性算法比通常的基于连续时间模型和离散时间模型的一致性算法更能提高多智能体网络的一致性收敛速度,而且还可以提高多智能体网络承受的最大时滞。
在多智能体网络中,智能体之间的信息通道不可避免地存在噪声,因此,智能体接受到的信息有时是被噪声“污染”的信息。很多专家研究了关于含有通讯噪声的一致性问题。由于多智能体网络经常收到外界的干扰,智能体之间的通讯链接关系可能随机断裂或重新建立。因此,很多学者研究具有随机拓扑结构的多智能体网络的一致性问题。现实中的多智能体网络同时受到“污染”信息和随机拓扑两种因素的影响,因此,本文在随机拓扑结构下研究了带有通讯噪声的一致性问题,并得到多智能体网络达到均方一致性和几乎必然一致性的条件。本文研究结果表明,在一致性算法中引入适当的衰减的增益因子后,多智能体网络即使在负的连接权重下依然可以取得一致性行为。
在现实生活中,由生物群体构成的系统都是耗散系统。复杂系统的耗散性对于智能体网络研究来说是个新问题。本文研究了关于时滞随机系统的耗散性,指数耗散性和镇定问题,取得了关于指数耗散性的一些条件,也讨论了随机时滞系统的无源性和非扩张性质,并且对所研究的时滞随机系统设计了切换控制器,运用李雅普诺夫方法导出其指数镇定的条件。
最后对全文进行了总结,并对今后的工作进行了展望。
In the past decades, distributed computing of networks mainly depends on some workstation consisting of both complex and expensive, but strong functional processors to carry out tasks. With the improvement of computer technology, complex dynamic systems rapidly develop in recent years. Superior performances of multi-agent networks based on complex dynamic systems as well as their more and more possible potential applications have been highlighted day by day. The same purpose can be obtained by using coordination between these simple and low-price agents, which not only save the cost, but enhance overall system's robustness and flexibility. Moreover, agents will be loss of energy during the process.Therefore, research on consensus and dissipativity of complex dynamic systems has aroused many experts' strong interest.The unprecedented upsurge has been raised to study complex dynamic systems in the world.
The dissertation has been focused on consensus problems in. singular systems, impulsive systems, as well as random network environment, by applying control theory, algebra graph theory as well as matrix theory, regarding some questions on network communication factors, such as time delay, noise, external disturbance under multi-agent networks as real backgrounds.
Since agents in networks not only accept information flow from their neighbor agents, but also suffer from the environment constrains, therefore the multi-agent networks may generally be described as singular systems.This dissertation has studied the multi-agent consensus problems based on singular systems for multi-agent networks, conditions for multi-agent systems to obtain consensus when singular systems are in present and absent of time delay, and then, maximum time delay the multi-agent networks can tolerate, as well as the worst speed convergent to consensus has been studied under the condition that multi-agent network can reach consensus.Robust consensus control problems have been studied when exterior disturbances and model uncertainty exist in the communication network under fixed and switched topologies.The results in this dissertation indicate that constraints from environments have influence on consensus behavior and performance of multi-agent networks.Maximum time-delay that multi-agent networks can tolerate as well as consensus convergence speed is related not only with Laplacian eigenvalues of multi-agent's network topology but also with constraints from network environments.
Recently, consensus algorithms are mainly based on continuous-time models and discrete-time models, but these models cannot contain some useful networks in the reality. In real dynamic networks, they are possibly some more complex systems, for example, switching systems or general hybrid systems. In real network, agents are subject to instantaneous disturbance frequently and change suddenly in certain time instant, i.e. they experience impulsive effect. Those phenomena widely exist in biological networks, flying objects and so on. Moreover, agents can obtain information from instantaneous contact with their neighbors. To make the best use of the information, impulsive consensus algorithms have been proposed for multi-agent networks in this dissertation. Consensus conditions, consensus convergence rate, as well as anti-disturbance ability have been studied under fixed and switched topologies for multi-agent networks. For multi-agent networks with time-delay, corresponding problems have been considered. The results in this dissertation indicate that consensus algorithms containing impulsive information have faster consensus convergence speed and bigger maximum time-delay that the multi-agent networks can tolerate than that in usual consensus algorithms of multi-agent network based on continuous-time or discrete-time models.
In multi-agent networks, noise is inevitable in information channels. Therefore, agents sometimes accept the information "polluted" by noise. Many experts are interested in consensus problems with communication noise. Since multi-agent networks frequently suffer from external disturbance, it is possible that link relations between agents are reconstructed or fail. Therefore, consensus problems of multi-agent networks with random topology have also been studied by many scholars. Two kinds of influence factors: "polluted" information and random topologies, are simultaneously in real multi-agent networks, therefore, consensus problems have been studied under random topology with communication noise in this dissertation. Conditions on mean square consensus and almost sure consensus have been obtained for multi-agent networks.The results indicate that multi-agent networks can still obtain consensus by applying consensus algorithms with suitable decreasing gain-factors, even if the multi-agent networks have negative connection weights.
In real world, systems consisting of groups of organisms are dissipative systems. Dissipativity of complex systems is a new problem for multi-agent networks. Dissipativity, exponential dissipation and stabilization are studied. Some conditions on dissipativity and exponential dissipativity are achieved. Passive and non-expansion properties are also discussed, and switching controllers are designed for the time- delay stochastic systems. Exponential stabilization conditions are derived by using the Lyapunov method in this dissertation.
Finally, a summary has been carried out in the dissertation and the further study has been presented.
本文以多智能体网络为实际背景,结合控制理论,代数图论以及矩阵论,围绕通讯网络存在的一些问题,如：时滞,噪声,外部干扰等因素,重点研究了基于奇异系统,脉冲系统,以及随机网络环境的一致性问题以及耗散性问题。
由于网络中的智能体不仅接受邻居智能体的信息流而且还受到环境的约束,因此一般情况下多智能体网络可描述为奇异系统。本文在环境约束下研究了基于奇异系统的多智能体网络的一致性问题,研究了在有或无时滞时多智能体网络取得一致性的条件,并研究了在取得一致性的前提下,多智能体网络可以承受的最大时滞,以及收敛到一致性的最差速度,最后研究了固定拓扑和切换拓扑下多智能体网络存在外部干扰和模型不确定性时的鲁棒一致性控制问题。本文研究结果表明,环境约束对多智能体网络取得一致性行为及其性能都有影响,多智能体网络可以承受的最大时滞以及收敛到一致性的速度不仅与多智能体的网络拓扑结构即网络图的拉普拉斯矩阵的特征值有关,而且与环境的约束条件有关。
目前研究一致性的算法基本上都是由连续时间模型或离散时间模型构成的,但是这些模型不能包含现实中一些有用的网络。现实的动态网络可能形成更加复杂的系统,例如切换系统,或更一般的混杂系统。在网络的动态变化过程中,智能体可能受到瞬间的干扰或在某些时刻经历突变,也就是说网络会出现脉冲效应,这些现象在飞行物运动网络,生物网络中广泛存在。在脉冲过程中,智能体可以从与邻居的瞬间接触中获取信息,为了充分利用所获得的信息,本文提出了多智能体网络的脉冲一致性算法,研究了在固定拓扑和切换拓扑结构下多智能体网络取得一致性的条件,一致性的收敛速度,以及抗干扰的能力,并在有时滞的多智能体网络中考虑了相应问题。本文研究结果表明,考虑脉冲信息的一致性算法比通常的基于连续时间模型和离散时间模型的一致性算法更能提高多智能体网络的一致性收敛速度,而且还可以提高多智能体网络承受的最大时滞。
在多智能体网络中,智能体之间的信息通道不可避免地存在噪声,因此,智能体接受到的信息有时是被噪声“污染”的信息。很多专家研究了关于含有通讯噪声的一致性问题。由于多智能体网络经常收到外界的干扰,智能体之间的通讯链接关系可能随机断裂或重新建立。因此,很多学者研究具有随机拓扑结构的多智能体网络的一致性问题。现实中的多智能体网络同时受到“污染”信息和随机拓扑两种因素的影响,因此,本文在随机拓扑结构下研究了带有通讯噪声的一致性问题,并得到多智能体网络达到均方一致性和几乎必然一致性的条件。本文研究结果表明,在一致性算法中引入适当的衰减的增益因子后,多智能体网络即使在负的连接权重下依然可以取得一致性行为。
在现实生活中,由生物群体构成的系统都是耗散系统。复杂系统的耗散性对于智能体网络研究来说是个新问题。本文研究了关于时滞随机系统的耗散性,指数耗散性和镇定问题,取得了关于指数耗散性的一些条件,也讨论了随机时滞系统的无源性和非扩张性质,并且对所研究的时滞随机系统设计了切换控制器,运用李雅普诺夫方法导出其指数镇定的条件。
最后对全文进行了总结,并对今后的工作进行了展望。
In the past decades, distributed computing of networks mainly depends on some workstation consisting of both complex and expensive, but strong functional processors to carry out tasks. With the improvement of computer technology, complex dynamic systems rapidly develop in recent years. Superior performances of multi-agent networks based on complex dynamic systems as well as their more and more possible potential applications have been highlighted day by day. The same purpose can be obtained by using coordination between these simple and low-price agents, which not only save the cost, but enhance overall system's robustness and flexibility. Moreover, agents will be loss of energy during the process.Therefore, research on consensus and dissipativity of complex dynamic systems has aroused many experts' strong interest.The unprecedented upsurge has been raised to study complex dynamic systems in the world.
The dissertation has been focused on consensus problems in. singular systems, impulsive systems, as well as random network environment, by applying control theory, algebra graph theory as well as matrix theory, regarding some questions on network communication factors, such as time delay, noise, external disturbance under multi-agent networks as real backgrounds.
Since agents in networks not only accept information flow from their neighbor agents, but also suffer from the environment constrains, therefore the multi-agent networks may generally be described as singular systems.This dissertation has studied the multi-agent consensus problems based on singular systems for multi-agent networks, conditions for multi-agent systems to obtain consensus when singular systems are in present and absent of time delay, and then, maximum time delay the multi-agent networks can tolerate, as well as the worst speed convergent to consensus has been studied under the condition that multi-agent network can reach consensus.Robust consensus control problems have been studied when exterior disturbances and model uncertainty exist in the communication network under fixed and switched topologies.The results in this dissertation indicate that constraints from environments have influence on consensus behavior and performance of multi-agent networks.Maximum time-delay that multi-agent networks can tolerate as well as consensus convergence speed is related not only with Laplacian eigenvalues of multi-agent's network topology but also with constraints from network environments.
Recently, consensus algorithms are mainly based on continuous-time models and discrete-time models, but these models cannot contain some useful networks in the reality. In real dynamic networks, they are possibly some more complex systems, for example, switching systems or general hybrid systems. In real network, agents are subject to instantaneous disturbance frequently and change suddenly in certain time instant, i.e. they experience impulsive effect. Those phenomena widely exist in biological networks, flying objects and so on. Moreover, agents can obtain information from instantaneous contact with their neighbors. To make the best use of the information, impulsive consensus algorithms have been proposed for multi-agent networks in this dissertation. Consensus conditions, consensus convergence rate, as well as anti-disturbance ability have been studied under fixed and switched topologies for multi-agent networks. For multi-agent networks with time-delay, corresponding problems have been considered. The results in this dissertation indicate that consensus algorithms containing impulsive information have faster consensus convergence speed and bigger maximum time-delay that the multi-agent networks can tolerate than that in usual consensus algorithms of multi-agent network based on continuous-time or discrete-time models.
In multi-agent networks, noise is inevitable in information channels. Therefore, agents sometimes accept the information "polluted" by noise. Many experts are interested in consensus problems with communication noise. Since multi-agent networks frequently suffer from external disturbance, it is possible that link relations between agents are reconstructed or fail. Therefore, consensus problems of multi-agent networks with random topology have also been studied by many scholars. Two kinds of influence factors: "polluted" information and random topologies, are simultaneously in real multi-agent networks, therefore, consensus problems have been studied under random topology with communication noise in this dissertation. Conditions on mean square consensus and almost sure consensus have been obtained for multi-agent networks.The results indicate that multi-agent networks can still obtain consensus by applying consensus algorithms with suitable decreasing gain-factors, even if the multi-agent networks have negative connection weights.
In real world, systems consisting of groups of organisms are dissipative systems. Dissipativity of complex systems is a new problem for multi-agent networks. Dissipativity, exponential dissipation and stabilization are studied. Some conditions on dissipativity and exponential dissipativity are achieved. Passive and non-expansion properties are also discussed, and switching controllers are designed for the time- delay stochastic systems. Exponential stabilization conditions are derived by using the Lyapunov method in this dissertation.
Finally, a summary has been carried out in the dissertation and the further study has been presented.
引文
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