【作者】 丁强；

【导师】 钟麦英；

【作者基本信息】 山东大学 ， 控制理论与控制工程， 2010， 博士

【摘要】 Markov跳跃系统是一类可用来描述因环境的突然变化、系统内部各子系统间联结方式的改变、非线性对象工作点范围的变化等导致结构发生随机突变的系统,如生产制造系统、电力系统、通讯系统、飞行器控制系统等。为了确保系统运行的安全性和可靠性,对于Markov跳跃系统鲁棒故障检测问题的研究具有重要的理论意义和实际应用价值。本文的主要目的是针对受L2范数有界未知输入、Polytopic型不确定性和时滞影响的Makrov跳跃系统以及受L2范数有界未知输入影响的一类奇异Markov跳跃系统,研究提出新的鲁棒故障检测方法,取得的主要成果包括：1.针对一类受L2范数有界未知输入影响的连续时间Markov系统,提出了基于自适应观测器的鲁棒故障检测方法。通过构造依赖系统模态的自适应Markov跳跃观测器作为残差产生器,将鲁棒故障检测滤波器的设计问题转化为随机H∞滤波问题。应用线性矩阵不等式技术推导并证明了问题可解的充分条件,得到了故障检测滤波器参数矩阵的解。2.对于受未知输入和Polytopic型不确定性影响的一类连续时间Markov跳跃系统,提出了故障检测问题的随机H∞滤波描述。同时考虑了模态在线可知和在线不可知两种情况,应用参数依赖的Lyapunov函数,通过引入松弛矩阵,推导并证明了问题可解的线性矩阵不等式充分条件。3.基于自适应观测器方法研究了时滞Markov跳跃系统的鲁棒故障检测问题。构造了含有状态时滞的自适应Markov跳跃观测器作为残差产生器。应用随机Lyapunov-Krasovskii函数方法,通过引入松弛矩阵,推导并证明了鲁棒故障检测滤波器存在的时滞依赖充分条件,给出了故障检测滤波器参数矩阵的求解方法。4.基于H∞滤波方法研究了一类受L2范数有界未知输入影响的连续时间奇异Markov跳跃系统鲁棒故障检测问题。同时考虑了模态在线可知和在线不可知两种情况,应用线性矩阵不等式技术推导了故障检测滤波器存在的充分条件,并给出了参数矩阵的求解方法。5.应用等价空间方法研究了一类离散时间Markov跳跃系统的故障检测和故障估计问题。对于故障检测问题,通过奇异值分解给出了等价矩阵的统一解及其参数化形式,并提出了一种减小矩阵运算量的递推算法；对于故障估计问题,通过引入新的设计准则来评估故障估计的性能,建立了故障估计问题和特定二次型最小化问题之间的关系,基于此得到了最小化问题可解的充分必要条件,并给出了等价矩阵的解析解形式。更多还原

【Abstract】 Markovian jump systems are demonstrated to be very appropriate to model plants whose structures are subject to random abrupt changes, due to, for instance, sudden environment changes, transition of subsystem interconnections, change of the operating point of a linearised model of a nonlinear systems, and so on. This kind of systems can be used to represent many important physical systems, such as manufacturing systems, electric power systems, communications systems, aircraft flight systems etc. In order to ensure the system safety and reliability, researches on robust fault detection for Markovian jump systems are not only theoretically interesting, but also very significant in practical applications. The purpose of this dissertation is to investigate fault detection for Markovian jump systems with L2-norm bounded unknown input, polytopic uncertainties, time-delays, and singular Markovian jump systems with L2-norm bounded unknown input. The main results of this dissertation are as follows.1. For a class of continuous-time Markovian systems with L2 norm bounded unknown input, an adaptive observer-based robust fault detection approach is proposed. By using a mode-dependent adaptive Markovian jump observer as residual generator, the robust fault detection filter design problem is formulated in the framework of stochastic H∞filtering problem. By applying linear matrix inequality technique, sufficient conditions on the existence of robust fault detection filter are derived, and the solutions are also given.2. For a class of continuous-time Markovian jump systems with both unknown inputs and Polytopic uncertainties, the stochastic H∞filtering formulation of fault detection is proposed. Both mode on-line available and on-line unavailable cases are considered, and by applying parameter-dependent stochastic Lyapunov function and introducing slack matrices, the solvable conditions of this problem are derived in terms of linear matrix inequalities.3. The problem of adaptive observer-based robust fault detection for time-delay Markovian jump systems. An adaptive Markovian jump observer with state delay is constructed as residual generator. Applying stochastic Lyapunov-Krasovskii functional approach and introducing slack matrices, delay-dependent sufficient conditions are derived to ensure that the robust fault detection filter design problem is solvable, and the solutions to the parameter matrices are also given.4. The problem of H∞filtering based robust fault detection for continuous-time singular Markovian jump systems is investigated. Both mode on-line available and on-line unavailable cases are considered, and sufficient conditions on the existence of the robust fault detection filter and parameter matrices to the fault detection filter are derived in terms of linear matrix inequalities.5. The problem of parity space-based fault detection and fault estimation problem for a class of discrete-time Markovian jump systems is studied. For fault detection problem, the unified solution to the parity matrices is given by using singular value decomposition, and a new recursive algorithm is developed to reduce the numerical computation. For fault estimation, some design criteria is introduced to evaluate the fault estimation performance index, and a relationship between the parity space-based fault estimation and the minimum problem of certain matrix quadratic form is built. Based on this, a necessary and sufficient condition for the minimum problem is derived, and a unified analytic solution to the parity matrices is obtained.更多还原