奇异系统的无源性与混沌系统的同步分析
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摘要
奇异非线性系统的无源性与混沌系统的同步分析是复杂系统控制理论中非常重要的研究领域.由于非线性系统的复杂性,奇异非线性系统无源性与混沌同步的研究还处在发展阶段,发展奇异非线性系统的无源控制与混沌同步的理论成为当前控制理论研究中的两项重要研究内容.目前,在奇异非线性系统的无源控制、非线性奇异摄动系统的无源性分析、混沌系统的耗散主从同步、离散混沌系统的脉冲同步和混沌系统驱动-响应同步的动态输出反馈控制器设计等方面尚有许多问题需要解决.本文的主要贡献在于：
(1)研究了带有非线性扰动的连续奇异系统的无源控制问题.使用Banach不动点原理、Picard-Lindelof定理和Lyapunov方法,导出了这类系统的无源性条件、解的存在唯一性条件和指数稳定性条件,首次获得了这些充分条件的统一线性矩阵不等式表示公式,并设计了状态反馈无源控制器.
(2)研究了不确定奇异摄动系统的无源性分析问题.基于Lyapunov稳定性理论和奇异系统的方法,首次将Klimushchev-Krasovskii引理用线性矩阵不等式表述.并基此给出了这类奇异摄动系统的无源性和渐近稳定性的充分条件,且通过求解广义特征值问题获得了不确定奇异摄动系统的最大稳定上界.
(3)研究了混沌系统在信息受限下的耗散主从同步问题.使用采样数据法、Lyapunov-Krasovskii方法和自由权矩阵技术,同时考虑传输诱导时滞、数据包丢失和量测量化,首次给出了混沌系统主从同步的线性矩阵不等式形式的耗散同步判据,并设计了混沌系统的耗散量化状态反馈控制器.
(4)研究了离散混沌系统在传输受限下的脉冲同步问题.使用量测反馈导出带有脉冲的控制律,并同时考虑量化误差的影响,首次导出了离散混沌系统在传输受限下的脉冲同步误差系统渐近稳定的线性矩阵不等式和代数不等式形式的充分条件.
(5)研究了混沌系统利用时变动态输出反馈的驱动-响应同步问题.基于Lyapunov-Krasovskii方法,首次得到了混沌系统利用时变时滞动态输出反馈的驱动-响应同步一个新的线性矩阵不等式形式的同步判据,并给出了混沌系统驱动-响应同步的时变动态输出反馈控制器存在的充分条件.
The passivity of singular nonlinear systems and the synchronization analysis of chaotic systems are very important research fields in the complex system control theory. Due to the complexity of the nonlinear system, the research on the passivity of singu-lar systems and the synchronization analysis of chaotic systems is now in a developing stage, development of passive control for singular systems and of chaos synchronization are of two important research contents in the control theory. At present, there are many problems to be solved, such as the passive control for the singular nonlinear systems, the passivity analysis of nonlinear singularly perturbed systems, the dissipative master-slave synchronization of chaotic systems, the impulsive synchronization of discrete-time chaotic systems, the dynamic output feedback controller design for drive-response synchroniza-tion of chaotic systems, and so on. The major contributions of this dissertation are as follows.
(1) The passive control problems are studied for the continuous singular systems with nonlinear perturbations. By using the Banach Fix-Point Principle, Picard-Lindelof Theorem and the Lyapunov approach, the passivity condition, the condition for the existence-uniqueness of solution and exponential stability condition are derived for this class of systems, and the unified formula which includes these sufficient conditions is firstly expressed in terms of linear matrix inequalities, then the state-feedback controller based on passivity is designed.
(2) The passivity analysis problems are addressed for the uncertain singularly perturbed systems. Based on Lyapunov stability theory and a singular system approach, the Klimushchev-Krasovskii Lemma is firstly formulated in terms of linear matrix inequalities, and some sufficient conditions of asymptotic stability and passivity for this class of systems are given, then the maximum stability bound for the uncertain singularly perturbed systems can be obtained via solving the generalized eigenvalue problem.
(3) The dissipative master-slave synchronization problems are investigated for chaotic systems under information constraints. By using sampled-data method, Lyapunov-Krasovskii approach and free weighting matrix technique, in which the transmission-induced time delay, data packet dropout and measurement quantization have been taken into consideration, the dissipative synchronization criterion for the master-slave synchronization of chaotic systems is firstly derived in the form of a linear ma-trix inequality, and the dissipative quantized state-feedback controller is designed.
(4) The impulsive synchronization problems are considered for the discrete-time chaotic systems subject to limited communication capacity. Control laws with impulses are derived by using measurement feedback, where the effect of quantization errors is considered, sufficient conditions for asymptotic stability of synchronization er-ror systems are firstly given in terms of linear matrix inequalities and algebraic inequalities.
(5) The drive-response synchronization problems are discussed for chaotic systems via time-varying dynamic output feedback controller. Based on the Lyapunov-Krasovskii approach, a novel synchronization criterion is firstly obtained and formulated in the form of a linear matrix inequality, and a sufficient condition on the existence of a time-varying dynamic output feedback controller is derived.
(1)研究了带有非线性扰动的连续奇异系统的无源控制问题.使用Banach不动点原理、Picard-Lindelof定理和Lyapunov方法,导出了这类系统的无源性条件、解的存在唯一性条件和指数稳定性条件,首次获得了这些充分条件的统一线性矩阵不等式表示公式,并设计了状态反馈无源控制器.
(2)研究了不确定奇异摄动系统的无源性分析问题.基于Lyapunov稳定性理论和奇异系统的方法,首次将Klimushchev-Krasovskii引理用线性矩阵不等式表述.并基此给出了这类奇异摄动系统的无源性和渐近稳定性的充分条件,且通过求解广义特征值问题获得了不确定奇异摄动系统的最大稳定上界.
(3)研究了混沌系统在信息受限下的耗散主从同步问题.使用采样数据法、Lyapunov-Krasovskii方法和自由权矩阵技术,同时考虑传输诱导时滞、数据包丢失和量测量化,首次给出了混沌系统主从同步的线性矩阵不等式形式的耗散同步判据,并设计了混沌系统的耗散量化状态反馈控制器.
(4)研究了离散混沌系统在传输受限下的脉冲同步问题.使用量测反馈导出带有脉冲的控制律,并同时考虑量化误差的影响,首次导出了离散混沌系统在传输受限下的脉冲同步误差系统渐近稳定的线性矩阵不等式和代数不等式形式的充分条件.
(5)研究了混沌系统利用时变动态输出反馈的驱动-响应同步问题.基于Lyapunov-Krasovskii方法,首次得到了混沌系统利用时变时滞动态输出反馈的驱动-响应同步一个新的线性矩阵不等式形式的同步判据,并给出了混沌系统驱动-响应同步的时变动态输出反馈控制器存在的充分条件.
The passivity of singular nonlinear systems and the synchronization analysis of chaotic systems are very important research fields in the complex system control theory. Due to the complexity of the nonlinear system, the research on the passivity of singu-lar systems and the synchronization analysis of chaotic systems is now in a developing stage, development of passive control for singular systems and of chaos synchronization are of two important research contents in the control theory. At present, there are many problems to be solved, such as the passive control for the singular nonlinear systems, the passivity analysis of nonlinear singularly perturbed systems, the dissipative master-slave synchronization of chaotic systems, the impulsive synchronization of discrete-time chaotic systems, the dynamic output feedback controller design for drive-response synchroniza-tion of chaotic systems, and so on. The major contributions of this dissertation are as follows.
(1) The passive control problems are studied for the continuous singular systems with nonlinear perturbations. By using the Banach Fix-Point Principle, Picard-Lindelof Theorem and the Lyapunov approach, the passivity condition, the condition for the existence-uniqueness of solution and exponential stability condition are derived for this class of systems, and the unified formula which includes these sufficient conditions is firstly expressed in terms of linear matrix inequalities, then the state-feedback controller based on passivity is designed.
(2) The passivity analysis problems are addressed for the uncertain singularly perturbed systems. Based on Lyapunov stability theory and a singular system approach, the Klimushchev-Krasovskii Lemma is firstly formulated in terms of linear matrix inequalities, and some sufficient conditions of asymptotic stability and passivity for this class of systems are given, then the maximum stability bound for the uncertain singularly perturbed systems can be obtained via solving the generalized eigenvalue problem.
(3) The dissipative master-slave synchronization problems are investigated for chaotic systems under information constraints. By using sampled-data method, Lyapunov-Krasovskii approach and free weighting matrix technique, in which the transmission-induced time delay, data packet dropout and measurement quantization have been taken into consideration, the dissipative synchronization criterion for the master-slave synchronization of chaotic systems is firstly derived in the form of a linear ma-trix inequality, and the dissipative quantized state-feedback controller is designed.
(4) The impulsive synchronization problems are considered for the discrete-time chaotic systems subject to limited communication capacity. Control laws with impulses are derived by using measurement feedback, where the effect of quantization errors is considered, sufficient conditions for asymptotic stability of synchronization er-ror systems are firstly given in terms of linear matrix inequalities and algebraic inequalities.
(5) The drive-response synchronization problems are discussed for chaotic systems via time-varying dynamic output feedback controller. Based on the Lyapunov-Krasovskii approach, a novel synchronization criterion is firstly obtained and formulated in the form of a linear matrix inequality, and a sufficient condition on the existence of a time-varying dynamic output feedback controller is derived.
引文
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