广义双线性Markov跳变系统的分析与控制
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摘要
广义双线性系统是最接近广义线性系统的一类广义非线性系统,非线性系统的理论分析与应用一直是控制领域研究的热点与难点。线性Markov跳变系统作为一种特殊的随机系统模型,凭借它强大的建模能力,吸引了众多专家学者的研究兴趣。本学位论文重点研究连续时间广义双线性Markov跳变系统的稳定性以及控制器和滤波器设计问题,并将其应用于系统的故障检测与鲁棒容错控制。更进一步的,把这些结论推广到带有时滞和参数不确定的广义双线性Markov跳变系统中去。主要的研究结果如下:
建立了广义双线性Markov跳变系统的数学模型,给出了系统随机可稳的定义。在此基础上,进行了状态反馈控制器和输出反馈控制器的设计,给出了控制器存在满足的线性矩阵不等式(LMIs)条件。进一步,将结论推广到参数不确定时滞广义双线性Markov跳变系统。
基于非线性系统鲁棒容错控制的概念,讨论了实现广义双线性Markov跳变系统鲁棒容错控制的反馈控制器的存在条件和设计方法,使设计的反馈控制器在正常情况下和存在执行器故障的情况下,都能保证闭环系统随机稳定并且满足L 2增益性能指标。
给出了广义双线性Markov跳变系统状态观测器的设计方法,进一步推导出满足要求的基于观测器的故障检测滤波器的存在条件。在此基础上,分别讨论了时滞广义双线性Markov跳变系统和参数不确定时滞广义双线性Markov跳变系统的鲁棒滤波问题。
建立了带有布朗运动的广义双线性Markov跳变系统的数学模型,并对其进行了稳定性分析。给出了状态观测器的存在条件和设计方法,并将结论推广到带有布朗运动的参数不确定广义双线性Markov跳变系统。
最后,对应的仿真实例验证了方法的有效性。
Singular bilinear system, different from a linear singular system, is a kind of nonlinear singular system. Control theories and applications of nonlinear systems have always been a hot research focus due to their potentials. Meanwhile, because of their capability of system modeling linear Markovian jump systems have also been extensively studied. The focus of this dissertation is stability analysis and controller and filter design of continuous singular bilinear Markovian jump systems (SBMJSs). Futhermore, fault detection and robust fault-tolerant control are discussed. The main contributions for this dissertation are as follows:
The model of SBMJSs is established and the stochastically stabilizable of SBMJSs is defined. According to this definition, state feedback controllers and output feedback controller are designed. Their existence conditions, described as LMIs, are given. Further, the design methods are extended into time-delay SBMJSs with parameter uncertainty.
Robust fault-tolerant control for SBMJSs is investigated and the proper controllers are designed. The controllers, whether the actuators are normal or abnormal, could be used to stabilize the closed-loop systems stochastically, and satify required L 2norm performance index.
State observers of SBMJSs are designed and applied to fault detection. Then the sufficient conditions of fault detection filter based on the observers are presented. According to this, the robust filtering problems of time-delay SBMJSs and time-delay SBMJSs with parameter uncertainty are discussed respectively.
The model of SBMJSs with Wiener process is established and a stable condition is given. Then observer of SBMJSs with Wiener process is designed to estimate state vector.
Finally, the corresponding numerical simulation illustrates the applicability and effectiveness of the techniques proposed above.
建立了广义双线性Markov跳变系统的数学模型,给出了系统随机可稳的定义。在此基础上,进行了状态反馈控制器和输出反馈控制器的设计,给出了控制器存在满足的线性矩阵不等式(LMIs)条件。进一步,将结论推广到参数不确定时滞广义双线性Markov跳变系统。
基于非线性系统鲁棒容错控制的概念,讨论了实现广义双线性Markov跳变系统鲁棒容错控制的反馈控制器的存在条件和设计方法,使设计的反馈控制器在正常情况下和存在执行器故障的情况下,都能保证闭环系统随机稳定并且满足L 2增益性能指标。
给出了广义双线性Markov跳变系统状态观测器的设计方法,进一步推导出满足要求的基于观测器的故障检测滤波器的存在条件。在此基础上,分别讨论了时滞广义双线性Markov跳变系统和参数不确定时滞广义双线性Markov跳变系统的鲁棒滤波问题。
建立了带有布朗运动的广义双线性Markov跳变系统的数学模型,并对其进行了稳定性分析。给出了状态观测器的存在条件和设计方法,并将结论推广到带有布朗运动的参数不确定广义双线性Markov跳变系统。
最后,对应的仿真实例验证了方法的有效性。
Singular bilinear system, different from a linear singular system, is a kind of nonlinear singular system. Control theories and applications of nonlinear systems have always been a hot research focus due to their potentials. Meanwhile, because of their capability of system modeling linear Markovian jump systems have also been extensively studied. The focus of this dissertation is stability analysis and controller and filter design of continuous singular bilinear Markovian jump systems (SBMJSs). Futhermore, fault detection and robust fault-tolerant control are discussed. The main contributions for this dissertation are as follows:
The model of SBMJSs is established and the stochastically stabilizable of SBMJSs is defined. According to this definition, state feedback controllers and output feedback controller are designed. Their existence conditions, described as LMIs, are given. Further, the design methods are extended into time-delay SBMJSs with parameter uncertainty.
Robust fault-tolerant control for SBMJSs is investigated and the proper controllers are designed. The controllers, whether the actuators are normal or abnormal, could be used to stabilize the closed-loop systems stochastically, and satify required L 2norm performance index.
State observers of SBMJSs are designed and applied to fault detection. Then the sufficient conditions of fault detection filter based on the observers are presented. According to this, the robust filtering problems of time-delay SBMJSs and time-delay SBMJSs with parameter uncertainty are discussed respectively.
The model of SBMJSs with Wiener process is established and a stable condition is given. Then observer of SBMJSs with Wiener process is designed to estimate state vector.
Finally, the corresponding numerical simulation illustrates the applicability and effectiveness of the techniques proposed above.
引文
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