应急控制中的阻隔控制策略
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摘要
阻隔控制作为应急控制的一种非常有效的方法已经在实际中被大量采用,例如传染病控制、网络蠕虫爆发控制和电力系统解列控制等,但关于该策略的系统理论尚未得到充分的探讨。本论文基于最优控制理论给出了动态隔离控制律的设计方法,讨论了最优隔离控制策略在SARS传播控制和蠕虫爆发控制中的应用。此外,利用图论理论也研究了在应急状态下基于大系统分割的阻隔策略。本论文是关于阻隔控制理论的初步研究,其主要内容如下:
1由于缺乏有效的疫苗和治疗手段,检疫隔离策略是控制SARS传播的最重要手段。本章基于一类SEQIJR传播模型,引入了表示检疫隔离策略的控制变量,讨论了动态检疫隔离策略在SARS传播控制中的应用。分别利用Pontryagin极大值原理和遗传算法给出了最优和次优控制律的设计方法。仿真结果验证了此最优和次优隔离控制的有效性,并且指出在传染病爆发的最初阶段实施最大强度控制具有非常重要的意义。这也解释了SARS爆发期间采取的“早发现,早隔离”这一强有力控制措施的重要性。此外,本章提出的次优控制方法不但其控制效果和代价非常接近于最优控制,而且形式较为简单,适用于实际的传染病控制。
2相对于第一部分对孤立单区域的研究,本部分重点研究由于人口流动而造成的SARS在多区域之间的传播及其相应的动态检疫隔离策略。建立了一类多区域的SARS传播模型,在模型中引入了表示各区域内检疫隔离策略的控制变量,而后利用Pontryagin极大值原理给出了动态最优隔离控制律的设计方法。结果表明本章提出的多区域传播模型很好地描述了SARS在区域之间的传播过程。此外,仿真结果不仅说明了在传染病爆发初期各区域内实施最大强度隔离控制的重要性而且也指出了区域间对检疫观察流动人口的必要性。同时这也解释了SARS爆发期间采取“早发现,早隔离”和区域间检疫隔离流动人口等防控措施对SARS疾病控制的重要性;
3基于Two-Factor传播模型讨论了动态隔离策略在网络蠕虫传播控制中的应用。在模型中引入了表示隔离策略的控制变量,分别利用Pontryagin极大值原理和遗传算法给出了最优和次优隔离控制律的设计方法。仿真结果验证了此最优和次优隔离控制的有效性,同时也说明了在蠕虫爆发初期实施最大强度隔离控制的重要性。
4引入基于系统分割的阻隔控制概念,利用图论理论讨论了在应急状态下大系统的分割问题,得到了可选和可行阻隔控制策略满足的必要条件,给出了阻隔控制策略的具体实施方案,将阻隔控制分为最优代价和时间优先两类,分别讨论了在网络蠕虫爆发控制和电力系统解列中的具体应用。
As a kind of effective emergency control, isolation control has been widely employed in practice, such as epidemics control, Internet worm outbreak control, power system splitting and etc. But the theory of this strategy has not been discussed systemically. In this dissertation, based on optimal control theory, the design of dynamic optimal isolation control laws is proposed. And the applications in SARS epidemics control and Internet worm control are discussed. Furthermore, based on graph theory, the islanding problems of large system under emergency are also investigated. This dissertation gives a pilot study on isolation control theory and the major works are as follows:
Firstly, in the absence of valid vaccine or medicines, quarantine and isolation strategies are the most important and effective measures against the outbreaks of SARS. Based on a SEQIJR transmission model, a control pair representing the quarantine and isolation strategies is introduced and incorporated in this model. And the application of the dynamic quarantine and isolation control for SARS epidemics control is discussed. The design of dynamic optimal and sub-optimal isolation control laws is proposed via Pontryagin's Maximum Principle and genetic algorithm, respectively. The simulation results illustrate the effectiveness of the optimal and sub-optimal strategies for outbreak control. And the results also demonstrate that the maximum implementations of quarantining and isolation strategies in the early stage of the epidemic are of very critical impacts in the both cases of optimal and sub-optimal control. This gives a theoretical interpretation to the practical experiences that the early quarantine and isolation strategies are critically important to control the outbreaks of epidemics. Furthermore, our results also show that the proposed sub-optimal control can lead to performances close to the optimal control, but with much simpler strategies for epidemics control in practical use.
Secondly, differed from the research on signal isolated region in first part, this part concerns the spread of disease from region to region by means of traveling population and related dynamic quarantine and isolation strategies. A multigroup SARS transmission model is constructed and pairs of control variables in terms of the quarantine and isolation strategies are introduced in this model. The optimal control laws in each region are obtained via the Pontryagin's Maximum Principle, The simulation results well illustrate how the disease spreads from region to region by means of traveling population. Furthermore, the results not only demonstrate the importance of the early quarantine and isolation strategies but also the necessity of the observation and quarantine of travelers between regions to control the outbreaks of epidemics. This gives theoretical interpretations to the practical experiences that the early quarantine and isolation strategies, as well as the observation and quarantine of travelers between regions, are critically important to contain the epidemic.
Thirdly, based on the Two-Factor transmission model, the application of the dynamic isolation control for network worm control is discussed. To this end, one control variable representing the isolation strategy is incorporated in the model. The optimal and sub-optimal isolation control laws are obtained via Pontryagin's Maximum Principle and genetic algorithm, respectively. The simulation results illustrate the effectiveness of the optimal and sub-optimal isolation strategies for worm outbreak control. And the results also demonstrate that the maximum implementation of isolation strategy in the early stage during the outbreak is critically important in worm control.
Finally, based on system islanding, the concept of isolation control is introduced. By graph theory, the islanding problems of large system under emergency are discussed. And necessary conditions of optional isolation strategy and feasible isolation strategy are proposed. Besides, two types of isolation schemes, optimal cost scheme and time primary scheme are proposed and employed in network worm control and power system splitting, respectively.
1由于缺乏有效的疫苗和治疗手段,检疫隔离策略是控制SARS传播的最重要手段。本章基于一类SEQIJR传播模型,引入了表示检疫隔离策略的控制变量,讨论了动态检疫隔离策略在SARS传播控制中的应用。分别利用Pontryagin极大值原理和遗传算法给出了最优和次优控制律的设计方法。仿真结果验证了此最优和次优隔离控制的有效性,并且指出在传染病爆发的最初阶段实施最大强度控制具有非常重要的意义。这也解释了SARS爆发期间采取的“早发现,早隔离”这一强有力控制措施的重要性。此外,本章提出的次优控制方法不但其控制效果和代价非常接近于最优控制,而且形式较为简单,适用于实际的传染病控制。
2相对于第一部分对孤立单区域的研究,本部分重点研究由于人口流动而造成的SARS在多区域之间的传播及其相应的动态检疫隔离策略。建立了一类多区域的SARS传播模型,在模型中引入了表示各区域内检疫隔离策略的控制变量,而后利用Pontryagin极大值原理给出了动态最优隔离控制律的设计方法。结果表明本章提出的多区域传播模型很好地描述了SARS在区域之间的传播过程。此外,仿真结果不仅说明了在传染病爆发初期各区域内实施最大强度隔离控制的重要性而且也指出了区域间对检疫观察流动人口的必要性。同时这也解释了SARS爆发期间采取“早发现,早隔离”和区域间检疫隔离流动人口等防控措施对SARS疾病控制的重要性;
3基于Two-Factor传播模型讨论了动态隔离策略在网络蠕虫传播控制中的应用。在模型中引入了表示隔离策略的控制变量,分别利用Pontryagin极大值原理和遗传算法给出了最优和次优隔离控制律的设计方法。仿真结果验证了此最优和次优隔离控制的有效性,同时也说明了在蠕虫爆发初期实施最大强度隔离控制的重要性。
4引入基于系统分割的阻隔控制概念,利用图论理论讨论了在应急状态下大系统的分割问题,得到了可选和可行阻隔控制策略满足的必要条件,给出了阻隔控制策略的具体实施方案,将阻隔控制分为最优代价和时间优先两类,分别讨论了在网络蠕虫爆发控制和电力系统解列中的具体应用。
As a kind of effective emergency control, isolation control has been widely employed in practice, such as epidemics control, Internet worm outbreak control, power system splitting and etc. But the theory of this strategy has not been discussed systemically. In this dissertation, based on optimal control theory, the design of dynamic optimal isolation control laws is proposed. And the applications in SARS epidemics control and Internet worm control are discussed. Furthermore, based on graph theory, the islanding problems of large system under emergency are also investigated. This dissertation gives a pilot study on isolation control theory and the major works are as follows:
Firstly, in the absence of valid vaccine or medicines, quarantine and isolation strategies are the most important and effective measures against the outbreaks of SARS. Based on a SEQIJR transmission model, a control pair representing the quarantine and isolation strategies is introduced and incorporated in this model. And the application of the dynamic quarantine and isolation control for SARS epidemics control is discussed. The design of dynamic optimal and sub-optimal isolation control laws is proposed via Pontryagin's Maximum Principle and genetic algorithm, respectively. The simulation results illustrate the effectiveness of the optimal and sub-optimal strategies for outbreak control. And the results also demonstrate that the maximum implementations of quarantining and isolation strategies in the early stage of the epidemic are of very critical impacts in the both cases of optimal and sub-optimal control. This gives a theoretical interpretation to the practical experiences that the early quarantine and isolation strategies are critically important to control the outbreaks of epidemics. Furthermore, our results also show that the proposed sub-optimal control can lead to performances close to the optimal control, but with much simpler strategies for epidemics control in practical use.
Secondly, differed from the research on signal isolated region in first part, this part concerns the spread of disease from region to region by means of traveling population and related dynamic quarantine and isolation strategies. A multigroup SARS transmission model is constructed and pairs of control variables in terms of the quarantine and isolation strategies are introduced in this model. The optimal control laws in each region are obtained via the Pontryagin's Maximum Principle, The simulation results well illustrate how the disease spreads from region to region by means of traveling population. Furthermore, the results not only demonstrate the importance of the early quarantine and isolation strategies but also the necessity of the observation and quarantine of travelers between regions to control the outbreaks of epidemics. This gives theoretical interpretations to the practical experiences that the early quarantine and isolation strategies, as well as the observation and quarantine of travelers between regions, are critically important to contain the epidemic.
Thirdly, based on the Two-Factor transmission model, the application of the dynamic isolation control for network worm control is discussed. To this end, one control variable representing the isolation strategy is incorporated in the model. The optimal and sub-optimal isolation control laws are obtained via Pontryagin's Maximum Principle and genetic algorithm, respectively. The simulation results illustrate the effectiveness of the optimal and sub-optimal isolation strategies for worm outbreak control. And the results also demonstrate that the maximum implementation of isolation strategy in the early stage during the outbreak is critically important in worm control.
Finally, based on system islanding, the concept of isolation control is introduced. By graph theory, the islanding problems of large system under emergency are discussed. And necessary conditions of optional isolation strategy and feasible isolation strategy are proposed. Besides, two types of isolation schemes, optimal cost scheme and time primary scheme are proposed and employed in network worm control and power system splitting, respectively.
引文
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