时滞切换系统H_∞故障估计问题研究
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摘要
随着科学技术的迅猛发展,服务于社会实践的系统越来越复杂,人们对系统安全性和可靠性的要求也越来越高。设备或某些元器件的故障不仅会影响系统的正常稳定运行,甚至可能造成人身伤亡和财产损失。借助于故障诊断系统,可以检测是否有故障发生,判断故障发生的位置及重要性,以及估计故障的形状、大小等,以避免灾难性事故的发生。因此故障检测与诊断技术对于现代高复杂性控制系统来说是极其重要和必不可少的。
另一方面,在实际工业领域中,许多控制系统的行为是由离散事件系统与连续变量系统相互作用而决定的,这类动态系统被称为混杂系统。切换系统是其中非常重要的一类。目前切换系统在控制领域已经显示出了越来越广泛的应用前景,引起了国内外众多研究人员的兴趣和关注,也取得了大量的研究成果,但现有文献所研究的问题主要集中在切换系统稳定性分析、切换系统关于外部输入的鲁棒性、切换控制器设计等方面,而对切换系统的故障诊断问题的研究还比较少。综上所述,针对切换系统进行故障诊断研究是十分必要的,其在理论研究和工程应用中都具有重要意义。
本文针对几类不同的线性和非线性时滞切换系统,研究了其H∞故障估计问题。论文的主要研究工作如下：
第二章利用共同Lyapunov函数法研究中立型切换Lur'e系统的故障估计问题。通过设计适当的基于观测器的故障估计器,将故障估计问题转化为H∞滤波问题。构造合适的Lyapunov-Krasovskii函数,在任意切换信号下得到该故障估计器存在的时滞依赖充分条件,并利用线性矩阵不等式技术给出估计器增益矩阵的求解方法。
第三章利用脉冲控制研究一类线性时滞切换系统的故障估计问题。通过构造由脉冲控制器和故障估计器组成的混杂控制器,得到更具有普遍意义的混杂系统—切换脉冲系统。利用多Lyapunov函数方法给出问题可解的时滞依赖充分条件,并根据锥形补方法得到相应的观测器增益矩阵和脉冲矩阵的求解迭代算法。
第四章基于最小驻留时间方法,对时滞切换Lur'e系统进行H∞故障估计问题的研究。在受限的切换信号作用下,通过构造切换故障估计器,推导并证明保证由原系统和故障估计系统组成的增广系统具有H∞性能的时滞依赖判据。在此基础上,应用线性矩阵不等式技术,给出相应的参数矩阵的解和切换信号需要满足的最小驻留时间条件。
第五章利用平均驻留时间方法,研究一类中立型非线性切换系统的故障估计问题。通过选取适当的加权函数,构造依赖于切换信号的故障估计器,应用Lyapunov-Krasovskii函数方法,得到问题可解的时滞依赖充分条件。同时利用锥形补线性化迭代算法,给出各参数矩阵的解以及切换信号需要满足的平均驻留时间条件。
第六章针对带有时变时滞信号的非线性切换系统,研究其降维故障估计器设计问题。通过设计基于观测器的切换估计器,应用平均驻留时间方法,得到保证估计误差系统指数稳定,同时满足给定的H∞性能指标的时滞依赖判据。在此基础上,通过求解一组凸最优化问题,得到降维估计器增益矩阵的解。
With the development of modern science and technology, there is an increasing demand for the complex and large-scale systems to be more safe, reliable and effec-tive. For safety-critical systems, the faults may result in human mortality, environ-ment impact and economic loss. Therefore, fault diagnosis technology is essential for modern highly complicated control systems. Fault diagnosis systems are used to detect faults and diagnose their location and significance in systems. A fault must be diagnosed as early as possible even it is tolerable at its early stage, so that any serious consequences can be avoided.
On another research front, it is more effective to describe complex engineering systems with inherently multimodal or variable structures as switched systems, such as the biochemical processes, the computer control systems and the communication industries. Compared with general systems, switched systems have the characteris-tics of complexity and peculiarity. Therefore, the study on switched systems is of great practical importance as well as theoretical significance, and has attracted ex-tensive attention over the past two decades. However, most of the important results obtained are concerned with stability analysis and controller design, the problem of fault diagnosis for switched systems are still open and challenging. Therefore, mo-tivated by the proceeding discussion, the topic of this research is focused on "Fault Estimation for Switched Time-delay Systems"
Chapter 2 is concerned with the problem of fault estimation for switched Lur'e systems with common Lyapunov functions approach. The main object is to design an observer-based fault estimator to ensure a prescribed H∞performance level. Suf-ficient delay-dependent existence conditions of the fault estimator are obtained by solving a set of linear matrix inequalities. Furthermore, a feasible solution to the H∞fault estimator gain matrices is proposed.
Chapter 3 addresses the problem of fault estimator design for switched time- delay systems with impulsive control. The impulsive behavior is introduced into a hybrid controller, which generates a novel class of hybrid systems called switched impulsive control systems. Some delay-dependent sufficient conditions are derived on the existence of the hybrid controller by using multiple Lyapunov functional ap-proach. In addition, based on cone complementarity algorithm, the solutions to ob-server gain matrices and the impulsive matrices are obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed approach.
Chapter 4 studies the problem of fault estimation for switched Lur'e systems based on minimal dwell time approach. The problem is formulated as to find a fault estimator to ensure both the absolute stability and a prescribed L2-gain bound of an augmented system from the original system and the fault estimation error system. Some delay-dependent sufficient conditions on the existence of an H∞fault estima-tor are derived. Associated solutions to the problem are obtained, and the minimal dwell time constraints are imposed for the switching rule.
Chapter 5 deals with the problem of fault estimation for a class of switched nonlinear systems of neutral type with average dwell time approach. By employ-ing a switched observer-based fault estimator, the problem is formulated as an H∞filtering problem. Sufficient delay-dependent existence conditions of the H∞fault estimator are given in terms of certain matrix inequalities. Moreover, the parameter matrices of the fault estimator and the suitable switching rule are obtained by using cone complementarity algorithm. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Chapter 6 investigates the problem of reduced-order fault estimator design for a class of switched nonlinear systems with time-varying delay. A generalized form of the observer-based reduced-order fault estimator is employed. Based on the aver-age dwell time approach and the Lyapunov functional technique, a sufficient delay-dependent criterion on the existence of the estimator is derived to ensure the expo-nential stability and a prescribed L2-gain bound of the error system. Furthermore, the parameters of an admissible estimator are obtained from the solution of a convex optimization problem. Numerical examples are provided to illustrate the effective-ness of the proposed results.
另一方面,在实际工业领域中,许多控制系统的行为是由离散事件系统与连续变量系统相互作用而决定的,这类动态系统被称为混杂系统。切换系统是其中非常重要的一类。目前切换系统在控制领域已经显示出了越来越广泛的应用前景,引起了国内外众多研究人员的兴趣和关注,也取得了大量的研究成果,但现有文献所研究的问题主要集中在切换系统稳定性分析、切换系统关于外部输入的鲁棒性、切换控制器设计等方面,而对切换系统的故障诊断问题的研究还比较少。综上所述,针对切换系统进行故障诊断研究是十分必要的,其在理论研究和工程应用中都具有重要意义。
本文针对几类不同的线性和非线性时滞切换系统,研究了其H∞故障估计问题。论文的主要研究工作如下：
第二章利用共同Lyapunov函数法研究中立型切换Lur'e系统的故障估计问题。通过设计适当的基于观测器的故障估计器,将故障估计问题转化为H∞滤波问题。构造合适的Lyapunov-Krasovskii函数,在任意切换信号下得到该故障估计器存在的时滞依赖充分条件,并利用线性矩阵不等式技术给出估计器增益矩阵的求解方法。
第三章利用脉冲控制研究一类线性时滞切换系统的故障估计问题。通过构造由脉冲控制器和故障估计器组成的混杂控制器,得到更具有普遍意义的混杂系统—切换脉冲系统。利用多Lyapunov函数方法给出问题可解的时滞依赖充分条件,并根据锥形补方法得到相应的观测器增益矩阵和脉冲矩阵的求解迭代算法。
第四章基于最小驻留时间方法,对时滞切换Lur'e系统进行H∞故障估计问题的研究。在受限的切换信号作用下,通过构造切换故障估计器,推导并证明保证由原系统和故障估计系统组成的增广系统具有H∞性能的时滞依赖判据。在此基础上,应用线性矩阵不等式技术,给出相应的参数矩阵的解和切换信号需要满足的最小驻留时间条件。
第五章利用平均驻留时间方法,研究一类中立型非线性切换系统的故障估计问题。通过选取适当的加权函数,构造依赖于切换信号的故障估计器,应用Lyapunov-Krasovskii函数方法,得到问题可解的时滞依赖充分条件。同时利用锥形补线性化迭代算法,给出各参数矩阵的解以及切换信号需要满足的平均驻留时间条件。
第六章针对带有时变时滞信号的非线性切换系统,研究其降维故障估计器设计问题。通过设计基于观测器的切换估计器,应用平均驻留时间方法,得到保证估计误差系统指数稳定,同时满足给定的H∞性能指标的时滞依赖判据。在此基础上,通过求解一组凸最优化问题,得到降维估计器增益矩阵的解。
With the development of modern science and technology, there is an increasing demand for the complex and large-scale systems to be more safe, reliable and effec-tive. For safety-critical systems, the faults may result in human mortality, environ-ment impact and economic loss. Therefore, fault diagnosis technology is essential for modern highly complicated control systems. Fault diagnosis systems are used to detect faults and diagnose their location and significance in systems. A fault must be diagnosed as early as possible even it is tolerable at its early stage, so that any serious consequences can be avoided.
On another research front, it is more effective to describe complex engineering systems with inherently multimodal or variable structures as switched systems, such as the biochemical processes, the computer control systems and the communication industries. Compared with general systems, switched systems have the characteris-tics of complexity and peculiarity. Therefore, the study on switched systems is of great practical importance as well as theoretical significance, and has attracted ex-tensive attention over the past two decades. However, most of the important results obtained are concerned with stability analysis and controller design, the problem of fault diagnosis for switched systems are still open and challenging. Therefore, mo-tivated by the proceeding discussion, the topic of this research is focused on "Fault Estimation for Switched Time-delay Systems"
Chapter 2 is concerned with the problem of fault estimation for switched Lur'e systems with common Lyapunov functions approach. The main object is to design an observer-based fault estimator to ensure a prescribed H∞performance level. Suf-ficient delay-dependent existence conditions of the fault estimator are obtained by solving a set of linear matrix inequalities. Furthermore, a feasible solution to the H∞fault estimator gain matrices is proposed.
Chapter 3 addresses the problem of fault estimator design for switched time- delay systems with impulsive control. The impulsive behavior is introduced into a hybrid controller, which generates a novel class of hybrid systems called switched impulsive control systems. Some delay-dependent sufficient conditions are derived on the existence of the hybrid controller by using multiple Lyapunov functional ap-proach. In addition, based on cone complementarity algorithm, the solutions to ob-server gain matrices and the impulsive matrices are obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed approach.
Chapter 4 studies the problem of fault estimation for switched Lur'e systems based on minimal dwell time approach. The problem is formulated as to find a fault estimator to ensure both the absolute stability and a prescribed L2-gain bound of an augmented system from the original system and the fault estimation error system. Some delay-dependent sufficient conditions on the existence of an H∞fault estima-tor are derived. Associated solutions to the problem are obtained, and the minimal dwell time constraints are imposed for the switching rule.
Chapter 5 deals with the problem of fault estimation for a class of switched nonlinear systems of neutral type with average dwell time approach. By employ-ing a switched observer-based fault estimator, the problem is formulated as an H∞filtering problem. Sufficient delay-dependent existence conditions of the H∞fault estimator are given in terms of certain matrix inequalities. Moreover, the parameter matrices of the fault estimator and the suitable switching rule are obtained by using cone complementarity algorithm. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.
Chapter 6 investigates the problem of reduced-order fault estimator design for a class of switched nonlinear systems with time-varying delay. A generalized form of the observer-based reduced-order fault estimator is employed. Based on the aver-age dwell time approach and the Lyapunov functional technique, a sufficient delay-dependent criterion on the existence of the estimator is derived to ensure the expo-nential stability and a prescribed L2-gain bound of the error system. Furthermore, the parameters of an admissible estimator are obtained from the solution of a convex optimization problem. Numerical examples are provided to illustrate the effective-ness of the proposed results.
引文
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