基于不完全测量信息的非线性随机系统的滤波与控制
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摘要
本文讨论基于不完全测量信息的几类非线性随机系统的滤波与控制问题。这里的不完全测量信息是指在建模过程中或者信息传输过程中由于受到物理设备限制或外加随机扰动而引起测量信号发生不可避免且通常无法预知的变化的现象,例如测量数据丢失、传感器延迟、信号量化、传感器饱和以及信号采样等。本文的主要内容分为三个部分。第一部分针对测量数据丢失、信号量化和传感器依概率延迟三种情形,研究几类具有一般形式的非线性随机离散系统的H∞滤波和控制问题,得到由HJI(Hamilton-Jacobi-Isaacs)不等式刻画的满足给定性能指标的滤波器或控制器的存在性条件。第二部分考虑几类特殊的非线性随机系统在有限时间域上的鲁棒H∞滤波问题。在研究过程中,我们首次提出并在数学上描述了一些新的测量信息不完全现象,如传感器依概率发生饱和以及系统中的非线性项以随机方式发生丢失等,并进一步给出上述情形下的非线性随机系统的滤波方法。第三部分,基于前两部分的研究结果,深入研究存在于传感器网络和复杂网络中的一些实际问题,设计符合指定性能指标的分布式滤波器和基于采样数据的控制器。具体而言,本文的框架可表述如下：
·第一章阐明本文所探索课题的研究意义、背景以及动机,介绍每一章节中所要研究的问题,并概括本文的主要贡献。
·第二章研究在数据依概率丢失情形下具有一般形式的一类非线性随机时滞网络化系统的量化H∞控制问题,得到由HJI不等式描述的关于量化H∞控制器存在性的分析结果,进而为几类特殊情形下的随机系统设计工程上易于实现的量化H∞控制器。
·第三章首先考虑在测量数据丢失情形下一类形式一般的非线性随机离散系统的H∞滤波问题,得到相应的由HJI不等式描述的H∞滤波器的存在性条件。然后,本章继续研究另一类非线性随机离散系统的H∞滤波问题,并考虑传感器在信号传输中随机发生时滞的现象。
·第四章研究在连续丢包并受信号量化影响情况下的一类非线性离散时变随机系统在有限时间域上的鲁棒H∞滤波问题。讨论非线性以随机方式发生的现象,并基于递推矩阵不等式为一类具有这种现象的时变系统设计滤波方法。
·第五章研究传感器以随机方式发生饱和的新现象,并结合测量数据丢失现象建立一个新的传感器模型,进一步探讨基于此类模型的H∞滤波问题。
·第六章针对传感器网络定义H∞一致性性能指标,定量地分析在有限时间域上滤波误差的有界一致性,研究在有限时间域上具有多重测量数据丢失情形下的传感器网络的分布式H∞一致性滤波问题,利用差分矩阵不等式技术设计鲁棒分布式H∞一致性滤波器。
·第七章研究传感器网络中一类多项式型非线性随机系统的分布式H∞滤波问题,使用具有多项式形式的Lyapunov函数分析滤波误差系统的稳定性,并通过求解一组依赖参数的矩阵不等式设计分布式H∞滤波器。
·第八章研究在随机采样数据情形下的传感器网络的分布式H∞滤波问题,通过把采样周期转化为有界时滞的方法分析滤波误差系统的H∞性能及其稳定性,并设计分布式H∞滤波器。
·第九章研究一类复杂动力网络的采样数据同步控制问题并设计采样数据同步控制器,考虑随机基因调控网络基于采样数据的H∞滤波问题并得到满足指定性能指标的滤波器,另外,讨论一类离散时变随机复杂网络在有限时间域上的同步与状态估计问题。
·第十章总结研究结果并讨论将来进一步要做的研究工作。
In this thesis, we discuss the filtering and control problems for several classes of nonlinear stochastic systems with incomplete information. The causes of incomplete information considered here include missing measurements, sensor delays, quantiza-tion effects, sensor saturations and signal sampling. The content of this thesis is mainly divided into three parts. In the first part, we focus on the H∞, filtering and control problems for some very general classes of nonlinear stochastic discrete-time systems subject to missing measurements, quantization effects and randomly varying sensor delays. Some sufficient conditions are derived for the existence of the desired filters and controllers in terms of the Hamilton-Jacobi-Isaacs (HJI) inequalities. The robust H∞filtering problems are considered in the second part for several special classes of nonlinear stochastic systems. In this part, some novel notions, including randomly occurring nonlinearities (RONs) and randomly occurring sensor satura-tions (ROSSs), are first put forward. Then, we develop a new filtering technique for the considered nonlinear stochastic systems with RONs, ROSSs as well as packet dropouts. In the third part, the theory and technique developed in previous parts are applied to deal with some issues in both sensor networks and complex networks and some desired distributed filters and sampled-data based controllers are designed. The compendious frame and description of the thesis are given as follows:
●In Chapter 1, the research background and motivation are discussed, the outline and contribution of the thesis are introduced, and the research problems to be addressed in each individual chapters are also outlined.
●In Chapter 2, we investigate the quantized H∞control problem for a class of nonlinear stochastic time-delay network-based systems with probabilistic data missing, where some analysis results on the existence of the quantized H∞controller are derived in terms of HJI inequalities. Based on the analysis results, some controllers are designed for some special classes of nonlinear stochastic systems.
●In Chapter 3, the H∞filtering problem is first investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements, and the existence condition of the desired H∞filter is obtained in terms of HJI inequalities. Then, the same problem is considered for the other class of non- linear stochastic systems where the phenomenon of randomly varying sensor delays is taken into account.
●In Chapter 4, we study the robust H∞finite-horizon filtering problem for a special class of nonlinear discrete time-varying stochastic systems with quanti-zation effects and successive packet dropouts, where a new phenomenon, that is, RON, is proposed and a new filtering approach is developed by employing the algorithm based on the recursive linear matrix inequalities.
●In Chapter 5, a new phenomenon of sensor saturation, namely, ROSS, is pro-posed and a novel sensor model is established to account for both the ROSS and missing measurement in a unified representation. Based on this sensor model, the H∞filtering problem is investigated for a class of nonlinear systems.
●In Chapter 6, a new notion of H∞-consensus performance requirement is de-fined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. Then, the distributed H∞-consensus filtering problem over a finite-horizon is studied for sensor networks with multiple missing mea-surements and some robust distributed H∞-consensus filters are designed by means of the solutions to a certain set of difference linear matrix inequalities.
●In Chapter 7, the distributed H∞filtering problem is addressed for a class of polynomial nonlinear stochastic systems in sensor networks. The Lyapunov function candidate with form of polynomials, is first adopted to analyze the stability of the filtering error system. Then, the desired distributed H∞filters are designed by solving a set of parameter-dependent linear matrix inequalities.
●In Chapter 8, the problem of distributed H∞filtering in sensor networks using a stochastic sampled-data approach is investigated. By using the method of converting the sampling periods into bounded time-delays, both of stability and H∞performance are analyzed for the filtering error system and a set of the desired distributed H∞filters is designed.
●Chapter 9 is concerned with the sampled-data synchronization control problem for a class of complex dynamic networks and a set of sampled-data synchroniza-tion controllers is designed. We also consider the sampled-data H∞filtering problem for a class of stochastic genetic regulatory networks. Moreover, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon.
●In Chapter 10, we summarize the results of the thesis and discuss some future work to be further investigated.
·第一章阐明本文所探索课题的研究意义、背景以及动机,介绍每一章节中所要研究的问题,并概括本文的主要贡献。
·第二章研究在数据依概率丢失情形下具有一般形式的一类非线性随机时滞网络化系统的量化H∞控制问题,得到由HJI不等式描述的关于量化H∞控制器存在性的分析结果,进而为几类特殊情形下的随机系统设计工程上易于实现的量化H∞控制器。
·第三章首先考虑在测量数据丢失情形下一类形式一般的非线性随机离散系统的H∞滤波问题,得到相应的由HJI不等式描述的H∞滤波器的存在性条件。然后,本章继续研究另一类非线性随机离散系统的H∞滤波问题,并考虑传感器在信号传输中随机发生时滞的现象。
·第四章研究在连续丢包并受信号量化影响情况下的一类非线性离散时变随机系统在有限时间域上的鲁棒H∞滤波问题。讨论非线性以随机方式发生的现象,并基于递推矩阵不等式为一类具有这种现象的时变系统设计滤波方法。
·第五章研究传感器以随机方式发生饱和的新现象,并结合测量数据丢失现象建立一个新的传感器模型,进一步探讨基于此类模型的H∞滤波问题。
·第六章针对传感器网络定义H∞一致性性能指标,定量地分析在有限时间域上滤波误差的有界一致性,研究在有限时间域上具有多重测量数据丢失情形下的传感器网络的分布式H∞一致性滤波问题,利用差分矩阵不等式技术设计鲁棒分布式H∞一致性滤波器。
·第七章研究传感器网络中一类多项式型非线性随机系统的分布式H∞滤波问题,使用具有多项式形式的Lyapunov函数分析滤波误差系统的稳定性,并通过求解一组依赖参数的矩阵不等式设计分布式H∞滤波器。
·第八章研究在随机采样数据情形下的传感器网络的分布式H∞滤波问题,通过把采样周期转化为有界时滞的方法分析滤波误差系统的H∞性能及其稳定性,并设计分布式H∞滤波器。
·第九章研究一类复杂动力网络的采样数据同步控制问题并设计采样数据同步控制器,考虑随机基因调控网络基于采样数据的H∞滤波问题并得到满足指定性能指标的滤波器,另外,讨论一类离散时变随机复杂网络在有限时间域上的同步与状态估计问题。
·第十章总结研究结果并讨论将来进一步要做的研究工作。
In this thesis, we discuss the filtering and control problems for several classes of nonlinear stochastic systems with incomplete information. The causes of incomplete information considered here include missing measurements, sensor delays, quantiza-tion effects, sensor saturations and signal sampling. The content of this thesis is mainly divided into three parts. In the first part, we focus on the H∞, filtering and control problems for some very general classes of nonlinear stochastic discrete-time systems subject to missing measurements, quantization effects and randomly varying sensor delays. Some sufficient conditions are derived for the existence of the desired filters and controllers in terms of the Hamilton-Jacobi-Isaacs (HJI) inequalities. The robust H∞filtering problems are considered in the second part for several special classes of nonlinear stochastic systems. In this part, some novel notions, including randomly occurring nonlinearities (RONs) and randomly occurring sensor satura-tions (ROSSs), are first put forward. Then, we develop a new filtering technique for the considered nonlinear stochastic systems with RONs, ROSSs as well as packet dropouts. In the third part, the theory and technique developed in previous parts are applied to deal with some issues in both sensor networks and complex networks and some desired distributed filters and sampled-data based controllers are designed. The compendious frame and description of the thesis are given as follows:
●In Chapter 1, the research background and motivation are discussed, the outline and contribution of the thesis are introduced, and the research problems to be addressed in each individual chapters are also outlined.
●In Chapter 2, we investigate the quantized H∞control problem for a class of nonlinear stochastic time-delay network-based systems with probabilistic data missing, where some analysis results on the existence of the quantized H∞controller are derived in terms of HJI inequalities. Based on the analysis results, some controllers are designed for some special classes of nonlinear stochastic systems.
●In Chapter 3, the H∞filtering problem is first investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements, and the existence condition of the desired H∞filter is obtained in terms of HJI inequalities. Then, the same problem is considered for the other class of non- linear stochastic systems where the phenomenon of randomly varying sensor delays is taken into account.
●In Chapter 4, we study the robust H∞finite-horizon filtering problem for a special class of nonlinear discrete time-varying stochastic systems with quanti-zation effects and successive packet dropouts, where a new phenomenon, that is, RON, is proposed and a new filtering approach is developed by employing the algorithm based on the recursive linear matrix inequalities.
●In Chapter 5, a new phenomenon of sensor saturation, namely, ROSS, is pro-posed and a novel sensor model is established to account for both the ROSS and missing measurement in a unified representation. Based on this sensor model, the H∞filtering problem is investigated for a class of nonlinear systems.
●In Chapter 6, a new notion of H∞-consensus performance requirement is de-fined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. Then, the distributed H∞-consensus filtering problem over a finite-horizon is studied for sensor networks with multiple missing mea-surements and some robust distributed H∞-consensus filters are designed by means of the solutions to a certain set of difference linear matrix inequalities.
●In Chapter 7, the distributed H∞filtering problem is addressed for a class of polynomial nonlinear stochastic systems in sensor networks. The Lyapunov function candidate with form of polynomials, is first adopted to analyze the stability of the filtering error system. Then, the desired distributed H∞filters are designed by solving a set of parameter-dependent linear matrix inequalities.
●In Chapter 8, the problem of distributed H∞filtering in sensor networks using a stochastic sampled-data approach is investigated. By using the method of converting the sampling periods into bounded time-delays, both of stability and H∞performance are analyzed for the filtering error system and a set of the desired distributed H∞filters is designed.
●Chapter 9 is concerned with the sampled-data synchronization control problem for a class of complex dynamic networks and a set of sampled-data synchroniza-tion controllers is designed. We also consider the sampled-data H∞filtering problem for a class of stochastic genetic regulatory networks. Moreover, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon.
●In Chapter 10, we summarize the results of the thesis and discuss some future work to be further investigated.
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