随机时滞网络控制系统的测量建模与估计问题的研究
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摘要
网络控制系统是当前控制领域的研究热点.然而,由于网络带宽有限以及信息传输过程中的碰撞,不可避免地导致信息延迟、数据包丢失、数据包时序错乱以及多包传输等问题.这些问题的存在破坏了系统性能,使得网络控制系统的分析和设计变得异常复杂.本文针对网络控制系统中存在的时延、数据包乱序等问题,首先研究由随机时滞引起的不确定测量的建模问题,然后在得到的测量模型的基础上提出了几类不同估计意义下的状态估计问题.主要研究内容如下：
1.在假设网络传输没有数据包丢失的前提下,针对随机时滞和数据包乱序的不确定测量建立两种测量模型.在每个时刻通过对收到的所有测量数据进行排列组合,给出一种不带时间戳的测量建模.另一种测量建模则是对已有文献中的带有时间戳的测量模型进行改进,保证每个测量输出仅被收到一次,且允许一次可以收到多个数据包,建立了一种更适合网络通信协议的测量模型.
2.利用不带时间戳的测量模型,研究一步滞后随机时滞的不稳定网络控制系统的最优状态估计问题.首先讨论同时收到两个测量数据出现乱序的情况,分别在两种不同的估计条件下设计最优估计器.这两种条件的主要区别在于是否保证估计误差协方差一致有界,通过证明得到在这两种估计条件下均能得到相同的估计器形式,即估计器端利用的测量值是收到的两个测量数据的平均值.最后根据收到测量数据的各种情况,给出最大随机时滞界为1时的最优状态估计器.
3.进一步分别研究最大随机时滞界N>1时不稳定和稳定的网络控制系统的最优状态估计问题.针对最大随机时滞界N>1时测量乱序会变得更加复杂的情况,首先利用FIFO原则限定突发乱序的测量,在误差协方差一致有界条件下得到估计器端利用的测量是所有测量数据的平均值的结果,从而得到不稳定系统的最优状态估计器；然后研究了去掉FIFO条件时,根据收到数据包个数和发生时滞的数据包个数之间的关系设计不稳定系统的最优状态估计器;最后将FIFO的结论推广到稳定系统中,即仅在保证无偏估计的意义下设计了有界随机时滞稳定系统的最优状态估计问题.
4.在假设随机时滞发生概率已知时,利用带有时间戳的测量模型,分别研究了网络控制系统的最优状态估计和H∞估计问题.将得到的随机时滞测量重组成无时滞的测量,利用新息重组的方法,给出了系统的最小方差估计；根据测量建模的特点,每一时刻的测量可以分为确定性和不确定性两部分,然后先设计基于确定性测量的估计,在此基础上再设计不确定测量的估计,最后得到H∞滤波器,并且保证闭环系统是指数均方稳定的.
5.针对带有有界随机时滞的网络控制系统,分别研究了最大时滞界为1和大于1两种情况下的基于观测器的H∞控制问题.首先利用带有时间戳的测量模型,得到每个时刻可能收到的测量值,依据确定性和不确定性测量数据依次设计状态观测器.最后通过求解线性矩阵不等式得到基于状态估计的控制器,使得闭环系统是指数均方稳定的,且满足设计的H∞控制性能γ.
Networked control system has attracted much attention in the current control field. However, as a direct consequence of finite bandwidth as well as the colli-sion in the process of information transmission, random delays, packet losses, out-of-sequence measurements and multiple-packet transmission are inevitable in net-worked systems. These problems destroy the performance of the system, even lead to system instability. The analysis and design of networked control system will become more complex. This paper proposes the random uncertain measurement model when there are random time delay and out-of-order measurements in net-worked transmission. Furthermore, the problems of state estimation are studied in some various senses for networked control system. The main contents of this paper are listed as follows:
1. Under the assumption of no packet loss, two measurement models are pre-sented for random delay and out-of-order measurement, respectively. By a set of permutations for all measurements at each time, the model is given without using time stamps; while the second model improves the pre-existing model with time stamp, it guarantees each packet must be received and only once, and it also allows to receive multiple packets once time. It is more suitable for network communication protocol.
2. The state estimation problem is studied for the unstable networked con-trol systems subject to one-step random delay by using measurements without time stamps. Firstly, we consider the case that two measurements are received at the same time with out-of-sequence, and design the optimal estimation under two different es-timate conditions. The primary difference between these two conditions is whether to guarantee estimation error covariance is uniformly bounded or not. The same es-timator form is obtained based on the average of all received measurements at each time. Finally, the estimator gains can be derived for one-step random delay.
3. The state estimation problem is further studied for the unstable and stable networked control systems subject to bounded random delay N>1, respectively. The problem of out-of-order measurement becomes more complex with bounded random delay N>1. With the assumption of FIFO principle, we then study the so-called unbiased, uniformly bounded linear state estimators and show that the es-timator structure is given based on the average of all received measurements at each time. Without the FIFO assumption, the optimal estimation is obtained for unstable system by analyzing the relation of the number of the received packets and delay packets. Finally, we generalize the results to stable system with FIFO, and get the optimal estimation only in the sense of unbiased.
4. With the given probability distribution of the random delays, the optimal estimation and H∞filtering are considered by the measurement model with time stamp, respectively. The measurement model with delays is written as an equiv-alent the measurement with delay free. Then the optimal estimator is derived by adopting a re-organized innovation analysis approach. For the measurements can be divided into certain and uncertain, we firstly design the estimator based on the certain measurement, then give the estimator by the uncertain part. Finally, H∞filtering is obtained and can be guaranteed the exponentially mean-square stability of the closed-loop system.
5. The observer-based H∞control problem is considered for networked control system subject to bounded random delay N=1and N>1, respectively. By the measurement model with time stamp, the state estimator is designed by certain mea-surement and uncertain measurement. Then the observer-based controller is obtained by solving linear matrix inequality, which guarantees the exponentially mean-square stability of the closed-loop system and satisfies the prescribed H∞performance.
1.在假设网络传输没有数据包丢失的前提下,针对随机时滞和数据包乱序的不确定测量建立两种测量模型.在每个时刻通过对收到的所有测量数据进行排列组合,给出一种不带时间戳的测量建模.另一种测量建模则是对已有文献中的带有时间戳的测量模型进行改进,保证每个测量输出仅被收到一次,且允许一次可以收到多个数据包,建立了一种更适合网络通信协议的测量模型.
2.利用不带时间戳的测量模型,研究一步滞后随机时滞的不稳定网络控制系统的最优状态估计问题.首先讨论同时收到两个测量数据出现乱序的情况,分别在两种不同的估计条件下设计最优估计器.这两种条件的主要区别在于是否保证估计误差协方差一致有界,通过证明得到在这两种估计条件下均能得到相同的估计器形式,即估计器端利用的测量值是收到的两个测量数据的平均值.最后根据收到测量数据的各种情况,给出最大随机时滞界为1时的最优状态估计器.
3.进一步分别研究最大随机时滞界N>1时不稳定和稳定的网络控制系统的最优状态估计问题.针对最大随机时滞界N>1时测量乱序会变得更加复杂的情况,首先利用FIFO原则限定突发乱序的测量,在误差协方差一致有界条件下得到估计器端利用的测量是所有测量数据的平均值的结果,从而得到不稳定系统的最优状态估计器；然后研究了去掉FIFO条件时,根据收到数据包个数和发生时滞的数据包个数之间的关系设计不稳定系统的最优状态估计器;最后将FIFO的结论推广到稳定系统中,即仅在保证无偏估计的意义下设计了有界随机时滞稳定系统的最优状态估计问题.
4.在假设随机时滞发生概率已知时,利用带有时间戳的测量模型,分别研究了网络控制系统的最优状态估计和H∞估计问题.将得到的随机时滞测量重组成无时滞的测量,利用新息重组的方法,给出了系统的最小方差估计；根据测量建模的特点,每一时刻的测量可以分为确定性和不确定性两部分,然后先设计基于确定性测量的估计,在此基础上再设计不确定测量的估计,最后得到H∞滤波器,并且保证闭环系统是指数均方稳定的.
5.针对带有有界随机时滞的网络控制系统,分别研究了最大时滞界为1和大于1两种情况下的基于观测器的H∞控制问题.首先利用带有时间戳的测量模型,得到每个时刻可能收到的测量值,依据确定性和不确定性测量数据依次设计状态观测器.最后通过求解线性矩阵不等式得到基于状态估计的控制器,使得闭环系统是指数均方稳定的,且满足设计的H∞控制性能γ.
Networked control system has attracted much attention in the current control field. However, as a direct consequence of finite bandwidth as well as the colli-sion in the process of information transmission, random delays, packet losses, out-of-sequence measurements and multiple-packet transmission are inevitable in net-worked systems. These problems destroy the performance of the system, even lead to system instability. The analysis and design of networked control system will become more complex. This paper proposes the random uncertain measurement model when there are random time delay and out-of-order measurements in net-worked transmission. Furthermore, the problems of state estimation are studied in some various senses for networked control system. The main contents of this paper are listed as follows:
1. Under the assumption of no packet loss, two measurement models are pre-sented for random delay and out-of-order measurement, respectively. By a set of permutations for all measurements at each time, the model is given without using time stamps; while the second model improves the pre-existing model with time stamp, it guarantees each packet must be received and only once, and it also allows to receive multiple packets once time. It is more suitable for network communication protocol.
2. The state estimation problem is studied for the unstable networked con-trol systems subject to one-step random delay by using measurements without time stamps. Firstly, we consider the case that two measurements are received at the same time with out-of-sequence, and design the optimal estimation under two different es-timate conditions. The primary difference between these two conditions is whether to guarantee estimation error covariance is uniformly bounded or not. The same es-timator form is obtained based on the average of all received measurements at each time. Finally, the estimator gains can be derived for one-step random delay.
3. The state estimation problem is further studied for the unstable and stable networked control systems subject to bounded random delay N>1, respectively. The problem of out-of-order measurement becomes more complex with bounded random delay N>1. With the assumption of FIFO principle, we then study the so-called unbiased, uniformly bounded linear state estimators and show that the es-timator structure is given based on the average of all received measurements at each time. Without the FIFO assumption, the optimal estimation is obtained for unstable system by analyzing the relation of the number of the received packets and delay packets. Finally, we generalize the results to stable system with FIFO, and get the optimal estimation only in the sense of unbiased.
4. With the given probability distribution of the random delays, the optimal estimation and H∞filtering are considered by the measurement model with time stamp, respectively. The measurement model with delays is written as an equiv-alent the measurement with delay free. Then the optimal estimator is derived by adopting a re-organized innovation analysis approach. For the measurements can be divided into certain and uncertain, we firstly design the estimator based on the certain measurement, then give the estimator by the uncertain part. Finally, H∞filtering is obtained and can be guaranteed the exponentially mean-square stability of the closed-loop system.
5. The observer-based H∞control problem is considered for networked control system subject to bounded random delay N=1and N>1, respectively. By the measurement model with time stamp, the state estimator is designed by certain mea-surement and uncertain measurement. Then the observer-based controller is obtained by solving linear matrix inequality, which guarantees the exponentially mean-square stability of the closed-loop system and satisfies the prescribed H∞performance.
引文
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