网络控制系统的稳定性分析及量化控制研究
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摘要
通过公共网络将控制对象、传感器、控制器和执行器连接起来构成的闭环反馈控制系统称为网络控制系统(Networked control systems、简称NCSs)。网络控制系统可以实现地域上广泛分布的控制节点之间的信息交换,这样就可以实现被控对象的实时反馈控制。与传统的点对点连接方式的控制系统相比,网络控制系统具有很多优点,它可以实现资源共享、进行远程操作与控制,安装与维护简便,系统构建模块化、集成化,成本比较低,故障诊断和维护比较方便,易扩展、灵活性强,可以有效改善传统控制系统布线成本高、可靠性差、不易扩展等弊端。近年来,网络控制系统受到广泛的关注,在航空航天、设备制造、过程控制、交通控制、经济管理、远程医疗以及危险、特殊环境等控制领域状得了广泛的应用。同时,对网络控制系统的分析和综合也一直是近年来国际控制领域的研究热点之一。IEEE SystemsMagazine和IEEE Trans.Automatic Control,Proceedings of the IEEE等权威杂志相继出版了网络控制系统研究方面的专刊,每年国内外举行的控制领域重要的国际会议也一直把网络控制系统的分析和综合作为一个很重要的专题来对待。
虽然网络控制系统具有很多优点,但是由于网络的介入,带来了许多新的问题和挑战,这些问题在传统的控制系统中一般不会出现或者可以忽略不计。这些问题主要包括:第一,网络诱导延迟。由于系统的各个节点通过公共网络进行连接,它们在地域上的分布可能非常广泛,因此输出信号和控制信号在网络中的传输时间不可忽略。网络延迟主要由三部分构成:数据从传感器到控制器的传输时间,控制器的计算时间和数据从控制器到执行器的传输时间。由于控制器的计算时间相对于其它两个来说一般比较小,因此在实际处理时经常将其忽略。这些延迟在传统的点对点控制系统中完全可以忽略不计。第二,数据丢包。由于公共网络的开放性和不可靠性,数据在传输过程中会不可避免的遇到数据拥塞等现象,从而出现数据丢失。丢包现象也是造成网络控制系统性能降低的因素之一。第三,数据错序。由于数据包在传输过程中会根据网络状况选择不同的路由,因此,后产生的数据可能会先到达目的端,从而产生数据包的时序错乱。第四,由于网络带宽和数据包大小的限制,一个相对大的数据包可能会被分为若干相对较小的数据包分别传输,而各个较小的数据包同时也面临着传输延迟和丢包等问题。这样在重新组包时就会面临部分数据缺失的问题。第五,数据量化。由于网络带宽的限制和传感器自身的限制,数据传输时的量化在所难免,因此还需要考虑量化作用对网络控制系统性能的影响。此外,相对于传统的控制系统,网络控制系统还存在着时钟异步,多速率采样的异步等问题。上面这些问题在传统的点对点控制系统中大都是不存在的,或者说可以忽略不计。因此,如何建立能反映网络控制系统基本特征的系统模型来应对这些问题成为一个非常迫切的任务。此外,由于一些在传统控制系统中广泛应用的方法在网络控制系统中不再适用,如何对现有的方法进行改进或者提出新的研究方法来分析网络控制系统也非常重要。
针对上面提到的这些问题,很多学者建立了各种网络控制系统的模型并采取不同的分析方法来研究这些问题。然而,由于模型的限制或者方法的限制,大多数学者在进行研究时都会建立一些假设,主要有:网络延迟小于一个采样周期,只有前馈网络通路或者只有反馈网络通路存在非理想网络状况,系统中只存在丢包现象或者只存在网络延迟,网络延迟或丢包满足给定的分布情况等等。这些假设会严重限制一些方法的应用范围,甚至使得一些结论只存在理论上的可行性。这些假设在很多情况下是不成立的,因此,对网络控制系统的研究还有待深入。
在本文所使用的网络控制系统模型中,上面提到的大部分假设我们都不需要。我们将网络延迟、数据丢包和数据错序等非理想网络状况统一到一个综合的性能指标中,该指标是时变的,并且可以大于一个采样周期。在第二章中,通过对矩阵函数的凸性质的利用,在李亚普诺夫泛函中引入网络延迟上界的信息,我们可以避免将时变延迟放大为其上界所引起的保守性问题。基于这种方法,我们研究了网络控制系统的稳定、镇定以及H_∞控制问题。文中给出的仿真实例表明该方法可以减少结果的保守性。
在第三章,本文所做的研究工作解决了下面几个在现有文献中广泛存在的问题。
1.在现有的一些文献中,作者一般假设网络延迟或者丢包严格小于某个值,当网络延迟或丢包个数小于该值时,利用他们的结论可以判断系统的稳定性。然而,我们知道,由于网络的不可靠性,网络延迟或者丢包个数偶尔会变得非常大,会远远大于给定的上界,此时,应用他们的结论就无法进行处理。
2.现有的一些网络控制系统的模型和分析方法只利用了网络延迟的上下界信息,对网络延迟在变化区间内的变化趋势以及分布情况没有给予足够的重视。针对上面提到的问题,除了网络延迟上下界的信息,本文还应用了网络延迟的值分布的信息,即网络延迟在不同区间的概率分布情况(本文所提到的网络延迟都是网络综合延迟,它包括了网络传输延迟、数据丢包和数据错序的信息)。存本文中,我们将网络延迟的变化区间分为高低两个区间并假设网络延迟落在两个区间的概率已知,即假设网络延迟的值分布信息已知。
应用值分布的信息,本文对网络控制系统进行重新建模,使得网络控制系统的模型能够反映网络延迟在区间内的变化趋势。通过构造新的李亚普诺夫泛函并应用新的分析方法,我们可以得到网络控制系统均方渐近稳定的稳定性判据。这些判据都是以线性矩阵不等式的形式给出的,可以很方便的利用Matlab中的LMI工具箱进行求解。不同于以往的结果,我们得到的充分条件的可解性不仅跟网络延迟的上下界有关,还跟网络延迟的值分布信息有关。此外,应用本文所建立的模型,我们可以允许大网络延迟的存在。通过本文的分析,我们可以得出以下结论:只要大的网络延迟发生的概率为0,即Prob{η(t)>ηM}=0(其中η(t)为时变延迟),η(t)的值可以取得非常大,对系统的均方稳定性没有任何影响。由于最大允许延迟的值对网络控制系统的控制性能没有影响,因此我们提出最大有效延迟的概念,定义使得Prob{η(t)>ηM)=0的最小的ηM为最大允许延迟。我们实际关心的是最大有效延迟的大小。通过文章最后给出的例子和仿真可以看出,应用本文的分析方法,在考虑网络延迟值分布信息的基础上,我们得到的最大有效延迟比现有结果好得多。
由于网络控制系统中的各控制节点大都是数字形式的处理器,因此需要将模拟信号转化成数字信号以及将数字信号转化成模拟信号,在转化过程中必然存在一个精度问题,由于传感器自身的精度限制以及成本的要求,这种转换不可能以无限的精度进行,数据的量化在所难免。另一方面,由于网络控制系统中使用的网络一般是公共网络,数据的传输信道会受到很大的限制,这也要求数据量化时的量化级数不能太高。因此,量化作用对网络控制系统的影响要比对传统控制系统的影响大得多,对网络控制系统中的量化控制理论的研究十分重要也十分必要。然而,在目前关于网络控制系统的研究中,大部分文献都假设数据在传输过程中是无损传输,即假设没有量化作用的存在。而在一些关于量化理论研究的文献中大都假设系统中不存在数据传输延迟,数据丢包等非理想网络因素的影响。当同时考虑非理想网络状况和量化作用的影响时,相关的研究工作还不是很多,不是很系统。
在本文的后两章,我们对网络控制系统的量化控制进行了系统的研究。首先,应用对数形式的量化器,在同时考虑前馈通路和反馈通路的量化影响和非理想网络环境影响时本文建立了网络控制系统的模型。基于这个模型,我们用扇形界的分析方法研究了网络控制系统的量化稳定性问题,并设计量化控制器对网络控制系统进行镇定。我们得到的系统的稳定性判据全部是以线性矩阵不等式的形式给出的,从得到的稳定性判据可以看出,不等式的可解性不仅跟网络延迟的上下界有关,还依赖于量化器的量化参数。当系统的状态不可得时,我们在第四章的后半部分研究了基于观测器的网络控制系统的量化输出反馈控制问题。在设计量化控制器和量化观测器时,我们提出了分离引理,可以很容易将控制增益和观测器增益分离到两个不同的矩阵不等式中,然后分别进行设计。
在第五章中,我们考虑了时变量化器的设计问题。首先,对离散网络控制系统,我们在考虑量化作用和非理想网络状况的前提下建立了网络控制系统的模型。并基于建立的模型研究了网络控制系统的量化镇定、量化H_∞最优控制、基于观测器的量化输出反馈控制以及动态量化输出反馈控制等问题。
The closed-loop control systems where the plant,sensor,controller and actuator are connected through shared network are called networked control systems(NCSs). Compared with the traditional point-to-point control systems,the advantages of NCSs lie on their high diagnostic capacity,easy installation and maintenance,low prices,few wires,high reliability,increased system agility,etc.Furthermore,by using NCSs,we can share the network resources and control the remote plant.Today,NCSs have a widely application in aerospace,equipment manufacturers,industrial process control,remote medical treatment and some dangerous and special environments.In recent years,the analysis and synthesis for NCSs have been absorbed considerable attention in the fields of engineering and control.Some important journals,such as IEEE Systems Magazine,IEEE Trans.Automatic Control and Proceedings of the IEEE,had published some special issues on the topic of NCSs in the past several years,which is also an important issue in some international proceedings.
However,the insertion of the network in the control systems brings some new challenging problems,these problems do not exist in the point-to-point control systems, which include:i) network-induced delay.The network nodes(sensor,controller, actuator and plant) may be far away from each other,therefore,the transmission time of the signal through the network can not be omitted.Generally speaking,the network-induced delay is composed of three parts,transmission time from sensor to controller,the computation time in the controller and transmission time from controller to actuator,ii) Packet dropout.Because of the unreliability of the network, signal may be lost in the process of transmission.The packet dropout can degrade the control performance of the NCSs.iii) Wrong packet sequence.In the process of transmission,the packets may be out of their original order because of choosing different route.That is,the packet which is sent out earlier may arrive at the destination later,iv) Due to the limited transmission capacity of the network,the big packet may be disassembled into several small packets before they are transmitted to the next node.And the small packets also meet the problems(i-iii) in the process of transmission,therefore,the integrity of the packet can not be guaranteed when assembled the small packets together,v) Data quantization.Because of the limited communication capacity of the network and the usage of the digital devices, the packet can not be transmitted without data quantization.Therefore,the effect of the quantization on the performance of the networked control systems should be considered.Furthermore,the asynchronous of clock and multi-rate sampling also make the analysis and control of NCSs complicated.Most of the problems referred above do not exist in the traditional point-to-point control systems,and some well established analysis methods in the traditional control systems will lose their effect in the networked control systems.Therefore,how to establish the NCSs model which can reflect the main characters of the network and propose some new analysis method to handle these problems are a hard task.
To solve the problems mentioned above,many kinds of NCSs models and analysis methods have been proposed in the past years.However,limited by the system model or analysis technology,the researchers make some assumptions in their papers, which include:the networked delay is less than one sampling period,the networked delay only exists in the forward network or in the backward network,there are only networked delay or packet dropout in the network,etc.These assumptions do not always hold in the practical systems,which limit the application of the obtained result severely.Furthermore,there are some assumptions which exist in most of the publications,for example,assume that all the networked delay smaller than a given bound and there is no quantization in the data transmission.Therefore,further research is still needed for the analysis and synthesis of networked control systems.
In the NCSs model used in this paper,most of the above mentioned assumptions can be removed.In Chapter 2,we firstly propose new type of Lyapunov functional, by using the convexity of matrix function,the conservatism caused by enlargingη(t) to its upper boundηM can be avoided.Based on this method,we also investigate the stability,stabilization and Hoo control of the networked control systems.The given examples illustrate the less conservativeness of the proposed method.
The following problems exist commonly in the published references,which are solved in Chapter 3.
1.In the published references,the authors often assume that all the networked delay is smaller than a given bound.However,as is known,because of the unreliability of the network,the delay can larger than the given bound.In this case,the obtained criteria in these references can not judge the stability of the NCSs.Therefore,new type of NCSs model and analysis methods are needed to solve this problem.
2.In the existing NCSs model and analysis method,only the variable range of the delay is utilized,the stochastic property of the delay has not caused enough attention.
In Chapter 3,besides the variable range of the delay,we also utilize the information of value distribution of it.Firstly,we divide the whole variable range of the delay into two subintervals and assume that the probability of the delay in different intervals are known a prior.The value distribution of the delay can reflect the quality of the network conditions rather than the variable range of it,detailed explain can be seen in Chapter 3.
By using the value distribution of the delay,we build new type of networked control systems.By using new Lyapunov functional and analysis method,we can obtain the sufficient condition for the mean square stability of the NCSs,which are shown in terms of linear matrix inequalities and can be easily solved by the LMI toolbox in Matlab.Different from the existing results,the solvability of our Conditions rely not only on the variation range of the delay,but also on the value distribution of it.Through the analysis of this paper,we can also conclude that if Prob{η(t) >ηM}=0,the large delay has no effect on the mean square stability performance of NCSs.From the above analysis,we can conclude that the maximum allowable bound of the delay appearing with a low probability has little effect on the system performance.Therefore,what we really concerned is the maximum effectual delay bound of the delay,that is,the minimumηM which makes Pr ob {η(t) >ηM}= 0.The numerical example shows that by using our method,the maximum efficiency delay bound is much better than the existing results.
In the networked control systems,quantization is inevitable from the following reasons.Firstly,controllers are usually implemented digitally,signals that take values in a continuous set need to be represented with finite precision to allow digital information precessing in finite time.Secondly,the limited capacity communication channel of the shared network can reflect the size of the signal.The effect of the quantization on the NCSs are much larger than the traditional control systems. However,up to now,when considering both effects of networked conditions and data quantization,the interrelated references are countable thus still needs further investigation.
In this paper,we make a systemic study for the quantization problem in NCSs. Firstly,considering the networked delay and data quantization in both forward and backward network,we establish the networked control system.Based on the proposed model,we study the stability of the networked control systems and design the quantized controller to stabilize of the system.The obtained criteria are shown in terms of linear matrix inequality.When the information of the state can not be measured,we also investigate the observer based quantized output controller design for the NCSs in Captor 4.A separation lemma is proposed to separate the controller gain and observer gain into different equations,which makes the design problem more easier.
In Captor 5,we consider the design problem of time-varying quantizer for NCSs. Firstly,considering the effect of data quantization and networked delay,we build the networked control system model.Based on this model,we study the quantized stabilization, quantized H_∞control of the NCSs.Furthermore,when the state information can not be measured,we also investigate the observer based quantized output feedback control and dynamic quantized output control problems.The numerical examples show that the obtained criteria can guarantee the stability of the NCSs.
虽然网络控制系统具有很多优点,但是由于网络的介入,带来了许多新的问题和挑战,这些问题在传统的控制系统中一般不会出现或者可以忽略不计。这些问题主要包括:第一,网络诱导延迟。由于系统的各个节点通过公共网络进行连接,它们在地域上的分布可能非常广泛,因此输出信号和控制信号在网络中的传输时间不可忽略。网络延迟主要由三部分构成:数据从传感器到控制器的传输时间,控制器的计算时间和数据从控制器到执行器的传输时间。由于控制器的计算时间相对于其它两个来说一般比较小,因此在实际处理时经常将其忽略。这些延迟在传统的点对点控制系统中完全可以忽略不计。第二,数据丢包。由于公共网络的开放性和不可靠性,数据在传输过程中会不可避免的遇到数据拥塞等现象,从而出现数据丢失。丢包现象也是造成网络控制系统性能降低的因素之一。第三,数据错序。由于数据包在传输过程中会根据网络状况选择不同的路由,因此,后产生的数据可能会先到达目的端,从而产生数据包的时序错乱。第四,由于网络带宽和数据包大小的限制,一个相对大的数据包可能会被分为若干相对较小的数据包分别传输,而各个较小的数据包同时也面临着传输延迟和丢包等问题。这样在重新组包时就会面临部分数据缺失的问题。第五,数据量化。由于网络带宽的限制和传感器自身的限制,数据传输时的量化在所难免,因此还需要考虑量化作用对网络控制系统性能的影响。此外,相对于传统的控制系统,网络控制系统还存在着时钟异步,多速率采样的异步等问题。上面这些问题在传统的点对点控制系统中大都是不存在的,或者说可以忽略不计。因此,如何建立能反映网络控制系统基本特征的系统模型来应对这些问题成为一个非常迫切的任务。此外,由于一些在传统控制系统中广泛应用的方法在网络控制系统中不再适用,如何对现有的方法进行改进或者提出新的研究方法来分析网络控制系统也非常重要。
针对上面提到的这些问题,很多学者建立了各种网络控制系统的模型并采取不同的分析方法来研究这些问题。然而,由于模型的限制或者方法的限制,大多数学者在进行研究时都会建立一些假设,主要有:网络延迟小于一个采样周期,只有前馈网络通路或者只有反馈网络通路存在非理想网络状况,系统中只存在丢包现象或者只存在网络延迟,网络延迟或丢包满足给定的分布情况等等。这些假设会严重限制一些方法的应用范围,甚至使得一些结论只存在理论上的可行性。这些假设在很多情况下是不成立的,因此,对网络控制系统的研究还有待深入。
在本文所使用的网络控制系统模型中,上面提到的大部分假设我们都不需要。我们将网络延迟、数据丢包和数据错序等非理想网络状况统一到一个综合的性能指标中,该指标是时变的,并且可以大于一个采样周期。在第二章中,通过对矩阵函数的凸性质的利用,在李亚普诺夫泛函中引入网络延迟上界的信息,我们可以避免将时变延迟放大为其上界所引起的保守性问题。基于这种方法,我们研究了网络控制系统的稳定、镇定以及H_∞控制问题。文中给出的仿真实例表明该方法可以减少结果的保守性。
在第三章,本文所做的研究工作解决了下面几个在现有文献中广泛存在的问题。
1.在现有的一些文献中,作者一般假设网络延迟或者丢包严格小于某个值,当网络延迟或丢包个数小于该值时,利用他们的结论可以判断系统的稳定性。然而,我们知道,由于网络的不可靠性,网络延迟或者丢包个数偶尔会变得非常大,会远远大于给定的上界,此时,应用他们的结论就无法进行处理。
2.现有的一些网络控制系统的模型和分析方法只利用了网络延迟的上下界信息,对网络延迟在变化区间内的变化趋势以及分布情况没有给予足够的重视。针对上面提到的问题,除了网络延迟上下界的信息,本文还应用了网络延迟的值分布的信息,即网络延迟在不同区间的概率分布情况(本文所提到的网络延迟都是网络综合延迟,它包括了网络传输延迟、数据丢包和数据错序的信息)。存本文中,我们将网络延迟的变化区间分为高低两个区间并假设网络延迟落在两个区间的概率已知,即假设网络延迟的值分布信息已知。
应用值分布的信息,本文对网络控制系统进行重新建模,使得网络控制系统的模型能够反映网络延迟在区间内的变化趋势。通过构造新的李亚普诺夫泛函并应用新的分析方法,我们可以得到网络控制系统均方渐近稳定的稳定性判据。这些判据都是以线性矩阵不等式的形式给出的,可以很方便的利用Matlab中的LMI工具箱进行求解。不同于以往的结果,我们得到的充分条件的可解性不仅跟网络延迟的上下界有关,还跟网络延迟的值分布信息有关。此外,应用本文所建立的模型,我们可以允许大网络延迟的存在。通过本文的分析,我们可以得出以下结论:只要大的网络延迟发生的概率为0,即Prob{η(t)>ηM}=0(其中η(t)为时变延迟),η(t)的值可以取得非常大,对系统的均方稳定性没有任何影响。由于最大允许延迟的值对网络控制系统的控制性能没有影响,因此我们提出最大有效延迟的概念,定义使得Prob{η(t)>ηM)=0的最小的ηM为最大允许延迟。我们实际关心的是最大有效延迟的大小。通过文章最后给出的例子和仿真可以看出,应用本文的分析方法,在考虑网络延迟值分布信息的基础上,我们得到的最大有效延迟比现有结果好得多。
由于网络控制系统中的各控制节点大都是数字形式的处理器,因此需要将模拟信号转化成数字信号以及将数字信号转化成模拟信号,在转化过程中必然存在一个精度问题,由于传感器自身的精度限制以及成本的要求,这种转换不可能以无限的精度进行,数据的量化在所难免。另一方面,由于网络控制系统中使用的网络一般是公共网络,数据的传输信道会受到很大的限制,这也要求数据量化时的量化级数不能太高。因此,量化作用对网络控制系统的影响要比对传统控制系统的影响大得多,对网络控制系统中的量化控制理论的研究十分重要也十分必要。然而,在目前关于网络控制系统的研究中,大部分文献都假设数据在传输过程中是无损传输,即假设没有量化作用的存在。而在一些关于量化理论研究的文献中大都假设系统中不存在数据传输延迟,数据丢包等非理想网络因素的影响。当同时考虑非理想网络状况和量化作用的影响时,相关的研究工作还不是很多,不是很系统。
在本文的后两章,我们对网络控制系统的量化控制进行了系统的研究。首先,应用对数形式的量化器,在同时考虑前馈通路和反馈通路的量化影响和非理想网络环境影响时本文建立了网络控制系统的模型。基于这个模型,我们用扇形界的分析方法研究了网络控制系统的量化稳定性问题,并设计量化控制器对网络控制系统进行镇定。我们得到的系统的稳定性判据全部是以线性矩阵不等式的形式给出的,从得到的稳定性判据可以看出,不等式的可解性不仅跟网络延迟的上下界有关,还依赖于量化器的量化参数。当系统的状态不可得时,我们在第四章的后半部分研究了基于观测器的网络控制系统的量化输出反馈控制问题。在设计量化控制器和量化观测器时,我们提出了分离引理,可以很容易将控制增益和观测器增益分离到两个不同的矩阵不等式中,然后分别进行设计。
在第五章中,我们考虑了时变量化器的设计问题。首先,对离散网络控制系统,我们在考虑量化作用和非理想网络状况的前提下建立了网络控制系统的模型。并基于建立的模型研究了网络控制系统的量化镇定、量化H_∞最优控制、基于观测器的量化输出反馈控制以及动态量化输出反馈控制等问题。
The closed-loop control systems where the plant,sensor,controller and actuator are connected through shared network are called networked control systems(NCSs). Compared with the traditional point-to-point control systems,the advantages of NCSs lie on their high diagnostic capacity,easy installation and maintenance,low prices,few wires,high reliability,increased system agility,etc.Furthermore,by using NCSs,we can share the network resources and control the remote plant.Today,NCSs have a widely application in aerospace,equipment manufacturers,industrial process control,remote medical treatment and some dangerous and special environments.In recent years,the analysis and synthesis for NCSs have been absorbed considerable attention in the fields of engineering and control.Some important journals,such as IEEE Systems Magazine,IEEE Trans.Automatic Control and Proceedings of the IEEE,had published some special issues on the topic of NCSs in the past several years,which is also an important issue in some international proceedings.
However,the insertion of the network in the control systems brings some new challenging problems,these problems do not exist in the point-to-point control systems, which include:i) network-induced delay.The network nodes(sensor,controller, actuator and plant) may be far away from each other,therefore,the transmission time of the signal through the network can not be omitted.Generally speaking,the network-induced delay is composed of three parts,transmission time from sensor to controller,the computation time in the controller and transmission time from controller to actuator,ii) Packet dropout.Because of the unreliability of the network, signal may be lost in the process of transmission.The packet dropout can degrade the control performance of the NCSs.iii) Wrong packet sequence.In the process of transmission,the packets may be out of their original order because of choosing different route.That is,the packet which is sent out earlier may arrive at the destination later,iv) Due to the limited transmission capacity of the network,the big packet may be disassembled into several small packets before they are transmitted to the next node.And the small packets also meet the problems(i-iii) in the process of transmission,therefore,the integrity of the packet can not be guaranteed when assembled the small packets together,v) Data quantization.Because of the limited communication capacity of the network and the usage of the digital devices, the packet can not be transmitted without data quantization.Therefore,the effect of the quantization on the performance of the networked control systems should be considered.Furthermore,the asynchronous of clock and multi-rate sampling also make the analysis and control of NCSs complicated.Most of the problems referred above do not exist in the traditional point-to-point control systems,and some well established analysis methods in the traditional control systems will lose their effect in the networked control systems.Therefore,how to establish the NCSs model which can reflect the main characters of the network and propose some new analysis method to handle these problems are a hard task.
To solve the problems mentioned above,many kinds of NCSs models and analysis methods have been proposed in the past years.However,limited by the system model or analysis technology,the researchers make some assumptions in their papers, which include:the networked delay is less than one sampling period,the networked delay only exists in the forward network or in the backward network,there are only networked delay or packet dropout in the network,etc.These assumptions do not always hold in the practical systems,which limit the application of the obtained result severely.Furthermore,there are some assumptions which exist in most of the publications,for example,assume that all the networked delay smaller than a given bound and there is no quantization in the data transmission.Therefore,further research is still needed for the analysis and synthesis of networked control systems.
In the NCSs model used in this paper,most of the above mentioned assumptions can be removed.In Chapter 2,we firstly propose new type of Lyapunov functional, by using the convexity of matrix function,the conservatism caused by enlargingη(t) to its upper boundηM can be avoided.Based on this method,we also investigate the stability,stabilization and Hoo control of the networked control systems.The given examples illustrate the less conservativeness of the proposed method.
The following problems exist commonly in the published references,which are solved in Chapter 3.
1.In the published references,the authors often assume that all the networked delay is smaller than a given bound.However,as is known,because of the unreliability of the network,the delay can larger than the given bound.In this case,the obtained criteria in these references can not judge the stability of the NCSs.Therefore,new type of NCSs model and analysis methods are needed to solve this problem.
2.In the existing NCSs model and analysis method,only the variable range of the delay is utilized,the stochastic property of the delay has not caused enough attention.
In Chapter 3,besides the variable range of the delay,we also utilize the information of value distribution of it.Firstly,we divide the whole variable range of the delay into two subintervals and assume that the probability of the delay in different intervals are known a prior.The value distribution of the delay can reflect the quality of the network conditions rather than the variable range of it,detailed explain can be seen in Chapter 3.
By using the value distribution of the delay,we build new type of networked control systems.By using new Lyapunov functional and analysis method,we can obtain the sufficient condition for the mean square stability of the NCSs,which are shown in terms of linear matrix inequalities and can be easily solved by the LMI toolbox in Matlab.Different from the existing results,the solvability of our Conditions rely not only on the variation range of the delay,but also on the value distribution of it.Through the analysis of this paper,we can also conclude that if Prob{η(t) >ηM}=0,the large delay has no effect on the mean square stability performance of NCSs.From the above analysis,we can conclude that the maximum allowable bound of the delay appearing with a low probability has little effect on the system performance.Therefore,what we really concerned is the maximum effectual delay bound of the delay,that is,the minimumηM which makes Pr ob {η(t) >ηM}= 0.The numerical example shows that by using our method,the maximum efficiency delay bound is much better than the existing results.
In the networked control systems,quantization is inevitable from the following reasons.Firstly,controllers are usually implemented digitally,signals that take values in a continuous set need to be represented with finite precision to allow digital information precessing in finite time.Secondly,the limited capacity communication channel of the shared network can reflect the size of the signal.The effect of the quantization on the NCSs are much larger than the traditional control systems. However,up to now,when considering both effects of networked conditions and data quantization,the interrelated references are countable thus still needs further investigation.
In this paper,we make a systemic study for the quantization problem in NCSs. Firstly,considering the networked delay and data quantization in both forward and backward network,we establish the networked control system.Based on the proposed model,we study the stability of the networked control systems and design the quantized controller to stabilize of the system.The obtained criteria are shown in terms of linear matrix inequality.When the information of the state can not be measured,we also investigate the observer based quantized output controller design for the NCSs in Captor 4.A separation lemma is proposed to separate the controller gain and observer gain into different equations,which makes the design problem more easier.
In Captor 5,we consider the design problem of time-varying quantizer for NCSs. Firstly,considering the effect of data quantization and networked delay,we build the networked control system model.Based on this model,we study the quantized stabilization, quantized H_∞control of the NCSs.Furthermore,when the state information can not be measured,we also investigate the observer based quantized output feedback control and dynamic quantized output control problems.The numerical examples show that the obtained criteria can guarantee the stability of the NCSs.
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