网络系统的性能分析与控制研究
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摘要
网络系统无处不在,宏观世界和微观世界的一切事物都可以用网络系统的观点去描述和分析。本文的研究涉及到了两类典型的网络系统：网络控制系统和无线传感器网络。在网络控制系统中,参考输入、对象输出和控制输入等信息通过网络在控制器、执行器和传感器之间传输,形成了更加灵活、功能更为强大的控制体系。网络化控制实现了资源的共享,降低了控制系统的复杂度和开发成本,近年来得到研究者的广泛关注。网络的引入既给控制系统带来了便利,同时也带来了新的挑战。一般来说,信号在网络中传输必然受到通讯因素的制约,进而影响网络控制系统的稳定和性能。目前网络控制系统的研究主要集中在基于状态空间法研究网络诱导参量,如时延对系统稳定性的影响,而基于频域最优控制的方法研究网络控制系统性能则较少。本文的研究从后者出发,通过研究网络控制系统的性能极限来揭示通讯信道特征参量与控制系统性能极限之间的内在联系。本文也研究了另外一类网络系统——无线传感器网络。无线传感器网络的研究涉及到电子电路、计算机科学、通讯理论、控制理论等领域,目前在各个学科领域都有大量的研究者从事相关工作。本文从复杂网络的角度出发建立无线传感器网络的模型,并利用复杂网络中常用的分析手段对无线传感器网络进行分析,解决无线传感器网络中网络性能与节点可用能量受限的矛盾,提高网络的使用寿命。全文主要内容概括如下：
研究了线性时不变、多输入多输出系统对随机信号的平均跟踪性能极限问题。考虑的随机参考输入信号为布朗运动。研究结果表明此类系统的跟踪性能极限完全由被控对象的结构特征和参考输入的统计特征决定。其中结构特征指被控对象的非最小相位零点和不稳定极点的位置和方向。作为特殊情形,给出了参考输入为一致随机信号以及被控对象仅含有单个非最小相位零点和单个不稳定极点时系统跟踪性能极限。最后,给出了两自由度控制器跟踪系统对随机信号的跟踪性能极限。
研究了线性时不变、多输入多输出、连续系统在输出反馈受到加性高斯噪声的干扰时的跟踪性能极限问题。也即求取系统跟踪布朗运动的最小误差值,其中布朗运动用于模拟确定性系统中的阶跃信号。这部分研究同时考虑了单位反馈和两自由度控制器结构。对于单位反馈结构,得到了跟踪性能极限的一个下界,而对于两自由度控制器结构,则得到了跟踪性能极限的精确值。所有结果表明高斯噪声与不稳定极点和非最小相位零点等对象内部结构特征相互作用,恶化了系统的跟踪性能。
研究了线性时不变、离散系统在输出反馈经过均匀量化器时的跟踪性能极限问题。考虑的系统为两自由度控制器结构,分别考虑单输入单输出和多输入多输出对象。结果表明量化的输出反馈使网络控制系统的跟踪性能变差。对于固定的量化间隔,跟踪性能恶化的程度取决于对象的内部结构特征。对于多输入多输出对象,合适选择量化方式能有效地降低量化带来的负面影响,提高系统的跟踪性能。
利用随机图的键逾渗模型为无线传感器网络建模。利用键逾渗模型的相变现象考察无线传感器网络中节点工作状态与网络连通性的关系,使得网络在保证连通性的同时降低节点能量消耗。提出了节点工作方式改进算法,使得整个网络的能量消耗更为均匀,延长了网络的使用寿命。
提出了一类复杂网络模型——多半径地理空间网络。研究了该模型的统计学特性并基于节点广播半径调节机制为无线传感器网络建模。通过分析和仿真证实采用多半径地理空间网络模型的无线传感器网络相对于传统节点等作用半径工作的无线传感器网络,具有更长的网络寿命和更快的数据传输速度。
最后对全文进行了总结,并对今后的研究工作进行了展望。
Networked systems are commonly seen in real world. All the things in both macrocosmos and microcosmos can be described and analyzed from the point view of networked systems. The discussions in this dissertation refer to two representative networked systems:networked control systems and wireless sensor networks. Reference input, plant output and control input signals are transmitted through networks between controllers, actors and sensors, which makes networked control systems more flexible with more powerful function. Networked control systems make it possible to share the resources, to reduce the complexity and producing costs, and thus, attract many attentions from researchers in recent years. Networks bring convenience to control systems, at the same time, it bring new challenges. Generally speaking, signals that transmitted in networks will also suffer the constraints originated from communication, which affect stability and performance of networked control systems. Recent studies are focused on stability of systems with considering networks induced parameters, such as time delay based on state space method. However, there are few works on the study of networked control systems performance based on frequency optimal control method. This dissertation addresses issues in this spirit, it try to establish the relationship between communication channel characteristic parameters and control systems performance through the analysis of limitations on networked control systems performance. Also, this dissertation studies another kind of networks and systems, which is wireless sensor networks. The studies on wireless sensor networks relate to knowledge in the field of electronic circuit, computer science, communication and control theory. Nowadays, the study on wireless sensor networks can be seen in many fields. From the view of complex networks, this dissertation establishes models of wireless sensor networks and gives the analysis by the tools that are commonly seen in complex networks analysis, which gives a way to solve the conflict between networks performance and limited nodes energy, and thus improves lifetime of wireless sensor networks. The main contents of this dissertation are outlined as follows.
Averaged tracking performance limitations in linear time invariant multi-input multi-output systems with random signal reference input has been studied. The random input signal considered is the Brownian motion sequence. Results show that tracking performance limitations in these kinds of systems depend on the structure of plant and statistic characteristics of reference input. Here the structure of plant refers to location and direction of nonminimum phase zeros and unstable poles. As special cases, this dissertation also studies tracking performance limitations when uniform random reference input and only single non-minimum phase zero with single unstable pole are considered. Finally, tracking performance limitations of two-degree-of-freedom controller tracking system with random reference input are given.
This dissertation studies the tracking performance limitations of linear time invariant, multi-input multi-output, continuous-time systems in which the output feedback is subject to an additive white Gaussian noise corruption. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. Both the unity feedback and two-degree-of-freedom controller structure are considered. In the former case this dissertation derives an explicit bound, and in the latter an exact expression of the minimal tracking error attainable under the noise effect. Both results demonstrate how the additive white Gaussian noise may degenerate the tracking performance, and how the noise effect may intertwine with unstable poles and nonminimum phase zeros which are intrinsic characteristics of the plant.
Also, this dissertation considers the issue of tracking performance limitations for linear time invariant discrete-time systems when the output feedback signal is subject to uniform quantization. Based on a two-degree-of-freedom controller structure, this dissertation addresses the issue in both single input single output and multi-input multi-output systems. Results show that quantization invariably degenerates the achievable tracking performance. For a certain quantization interval, the extent of degeneration depends on the structure of the underlying system. For multi-input multi-output plant, it is found that a proper choice of the quantization method could reduce the negative effect of quantization, and thus improve the best tracking performance.
Based on site percolation model, which is a special kind of random graphs, this dissertation establishes a model for wireless sensor networks. Relationship between work mode of node and connectivity of networks has been studied with the aid of phase transition phenomena in site percolation model, which reduces energy consumption of nodes and guarantees connectivity of networks. Furthermore, an algorithm has been proposed to mend the work mode of node. As a result, energy consumption becomes more averaged, and thus lifetime of networks is prolonged.
A new kind of complex networks model named multi-radius geographical spatial network model has been proposed. This dissertation studies statistic characteristics of this model and then proposes an efficient mechanism of broadcasting radius adjustment that maps sensor networks to multi-radius geographical spatial networks. Analysis and simulation show that sensor networks working under our mechanism could consume energy uniformly to prolong lifetime of networks and have faster data delivering speed than those in traditional uniform radius sensor networks.
Finally, a summary for all discussions is given in the dissertation. Future works that related to this work are also presented.
研究了线性时不变、多输入多输出系统对随机信号的平均跟踪性能极限问题。考虑的随机参考输入信号为布朗运动。研究结果表明此类系统的跟踪性能极限完全由被控对象的结构特征和参考输入的统计特征决定。其中结构特征指被控对象的非最小相位零点和不稳定极点的位置和方向。作为特殊情形,给出了参考输入为一致随机信号以及被控对象仅含有单个非最小相位零点和单个不稳定极点时系统跟踪性能极限。最后,给出了两自由度控制器跟踪系统对随机信号的跟踪性能极限。
研究了线性时不变、多输入多输出、连续系统在输出反馈受到加性高斯噪声的干扰时的跟踪性能极限问题。也即求取系统跟踪布朗运动的最小误差值,其中布朗运动用于模拟确定性系统中的阶跃信号。这部分研究同时考虑了单位反馈和两自由度控制器结构。对于单位反馈结构,得到了跟踪性能极限的一个下界,而对于两自由度控制器结构,则得到了跟踪性能极限的精确值。所有结果表明高斯噪声与不稳定极点和非最小相位零点等对象内部结构特征相互作用,恶化了系统的跟踪性能。
研究了线性时不变、离散系统在输出反馈经过均匀量化器时的跟踪性能极限问题。考虑的系统为两自由度控制器结构,分别考虑单输入单输出和多输入多输出对象。结果表明量化的输出反馈使网络控制系统的跟踪性能变差。对于固定的量化间隔,跟踪性能恶化的程度取决于对象的内部结构特征。对于多输入多输出对象,合适选择量化方式能有效地降低量化带来的负面影响,提高系统的跟踪性能。
利用随机图的键逾渗模型为无线传感器网络建模。利用键逾渗模型的相变现象考察无线传感器网络中节点工作状态与网络连通性的关系,使得网络在保证连通性的同时降低节点能量消耗。提出了节点工作方式改进算法,使得整个网络的能量消耗更为均匀,延长了网络的使用寿命。
提出了一类复杂网络模型——多半径地理空间网络。研究了该模型的统计学特性并基于节点广播半径调节机制为无线传感器网络建模。通过分析和仿真证实采用多半径地理空间网络模型的无线传感器网络相对于传统节点等作用半径工作的无线传感器网络,具有更长的网络寿命和更快的数据传输速度。
最后对全文进行了总结,并对今后的研究工作进行了展望。
Networked systems are commonly seen in real world. All the things in both macrocosmos and microcosmos can be described and analyzed from the point view of networked systems. The discussions in this dissertation refer to two representative networked systems:networked control systems and wireless sensor networks. Reference input, plant output and control input signals are transmitted through networks between controllers, actors and sensors, which makes networked control systems more flexible with more powerful function. Networked control systems make it possible to share the resources, to reduce the complexity and producing costs, and thus, attract many attentions from researchers in recent years. Networks bring convenience to control systems, at the same time, it bring new challenges. Generally speaking, signals that transmitted in networks will also suffer the constraints originated from communication, which affect stability and performance of networked control systems. Recent studies are focused on stability of systems with considering networks induced parameters, such as time delay based on state space method. However, there are few works on the study of networked control systems performance based on frequency optimal control method. This dissertation addresses issues in this spirit, it try to establish the relationship between communication channel characteristic parameters and control systems performance through the analysis of limitations on networked control systems performance. Also, this dissertation studies another kind of networks and systems, which is wireless sensor networks. The studies on wireless sensor networks relate to knowledge in the field of electronic circuit, computer science, communication and control theory. Nowadays, the study on wireless sensor networks can be seen in many fields. From the view of complex networks, this dissertation establishes models of wireless sensor networks and gives the analysis by the tools that are commonly seen in complex networks analysis, which gives a way to solve the conflict between networks performance and limited nodes energy, and thus improves lifetime of wireless sensor networks. The main contents of this dissertation are outlined as follows.
Averaged tracking performance limitations in linear time invariant multi-input multi-output systems with random signal reference input has been studied. The random input signal considered is the Brownian motion sequence. Results show that tracking performance limitations in these kinds of systems depend on the structure of plant and statistic characteristics of reference input. Here the structure of plant refers to location and direction of nonminimum phase zeros and unstable poles. As special cases, this dissertation also studies tracking performance limitations when uniform random reference input and only single non-minimum phase zero with single unstable pole are considered. Finally, tracking performance limitations of two-degree-of-freedom controller tracking system with random reference input are given.
This dissertation studies the tracking performance limitations of linear time invariant, multi-input multi-output, continuous-time systems in which the output feedback is subject to an additive white Gaussian noise corruption. The problem under consideration amounts to determining the minimal error in tracking a Brownian motion random process, which emulates a step reference signal in the deterministic setting. Both the unity feedback and two-degree-of-freedom controller structure are considered. In the former case this dissertation derives an explicit bound, and in the latter an exact expression of the minimal tracking error attainable under the noise effect. Both results demonstrate how the additive white Gaussian noise may degenerate the tracking performance, and how the noise effect may intertwine with unstable poles and nonminimum phase zeros which are intrinsic characteristics of the plant.
Also, this dissertation considers the issue of tracking performance limitations for linear time invariant discrete-time systems when the output feedback signal is subject to uniform quantization. Based on a two-degree-of-freedom controller structure, this dissertation addresses the issue in both single input single output and multi-input multi-output systems. Results show that quantization invariably degenerates the achievable tracking performance. For a certain quantization interval, the extent of degeneration depends on the structure of the underlying system. For multi-input multi-output plant, it is found that a proper choice of the quantization method could reduce the negative effect of quantization, and thus improve the best tracking performance.
Based on site percolation model, which is a special kind of random graphs, this dissertation establishes a model for wireless sensor networks. Relationship between work mode of node and connectivity of networks has been studied with the aid of phase transition phenomena in site percolation model, which reduces energy consumption of nodes and guarantees connectivity of networks. Furthermore, an algorithm has been proposed to mend the work mode of node. As a result, energy consumption becomes more averaged, and thus lifetime of networks is prolonged.
A new kind of complex networks model named multi-radius geographical spatial network model has been proposed. This dissertation studies statistic characteristics of this model and then proposes an efficient mechanism of broadcasting radius adjustment that maps sensor networks to multi-radius geographical spatial networks. Analysis and simulation show that sensor networks working under our mechanism could consume energy uniformly to prolong lifetime of networks and have faster data delivering speed than those in traditional uniform radius sensor networks.
Finally, a summary for all discussions is given in the dissertation. Future works that related to this work are also presented.
引文
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