| 随机非线性系统的控制器设计和闭环性能分析 |
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| 引用本文： | 刘淑君,张纪峰.随机非线性系统的控制器设计和闭环性能分析[J].中国科学院研究生院学报,2010,27(5):711-719. |
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| 作者姓名： | 刘淑君 张纪峰 |
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| 作者单位： | 中国科学院数学与系统科学研究院系统控制重点实验室,北京,100190 |
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| 摘 要： | 针对几类重要的随机非线性系统, 提出了一些新的概念,发展了一些基本分析工具, 研究了几类控制器的设计问题. 主要成果包括:(1) 针对一类部分动态不可量测的非线性随机系统,引入了随机输入状态稳定(SISS)的概念, 借助于分析概率理论,发展了随机系统改变能量函数方法, 成功地处理了随机微分中的伊藤项,给出了随机非线性串联系统SISS的小增益类条件. (2) 对一类具有SISS随机逆动态的大规模随机非线性系统,给出了分散自适应输出反馈镇定控制器的构造性设计方法. 既解决了实用镇定问题也解决了渐近镇定问题. 在分散控制框架内,给出了处理随机非线性逆动 态的方法. (3) 对一类具有不稳定零动态的随机非线性系统,引入了随机输入状态可镇定的概念,给出了全局输出反馈镇定控制器构造性设计方法. (4) 对一类具有线性增长的不可量测状态的随机非线性系统,针对方差未知的噪声和一般随机输入,引入了广义随机输入状态稳定(GSISS)的概念,分别给出了随机干扰抑制和渐近镇定的输出反馈控制器的构造性设计方法.(5) 对一般的时滞随机非线性系统, 给出了解存在唯一的判定条件,引入了依概率全局(渐近)稳定的概念及相应的判定准则,丰富了随机时滞非线性系统的控制器设计理论. 对一类不确定随机时变时滞系统,构造性地设计出了自适应输出反馈镇定控制器.
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| 关 键 词： | 随机非线性系统 零动态 逆动态 输出反馈 积分反推法 镇定控制器 严格反馈 随机输入状态稳定 |
| 收稿时间： | 2010-01-08 |
Controller design for stochastic nonlinear systems and performance analysis of the closed-loop systems |
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| LIU Shu-Jun,ZHANG Ji-Feng.Controller design for stochastic nonlinear systems and performance analysis of the closed-loop systems[J].Journal of the Graduate School of the Chinese Academy of Sciences,2010,27(5):711-719. |
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| Authors: | LIU Shu-Jun ZHANG Ji-Feng |
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| Institution: | Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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| Abstract: | For several classes of important stochastic nonlinear systems we develop new concepts and basic analysis tools, based on which some problems of controller design are investigated and solved. The main contents are the following. (1) For a class of stochastic nonlinear systems with unmeasurable dynamics, the concept of stochastic input-to-state stability (SISS) is introduced. By using the probability theory, a method of changing supply functions is developed in the stochastic framework, and a small-gain condition on the SISS is given for cascaded stochastic nonlinear systems. (2) For a class of large-scale stochastic nonlinear systems with SISS stochastic inverse dynamics, a decentralized adaptive stabilization controller based on output feedback is constructively designed. Both practical stabilization and asymptotical stabilization are solved. A method dealing with the stochastic nonlinear inverse dynamics is given in the framework of decentralized control. (3) For a class of stochastic nonlinear systems with unstable zero dynamics, the concept of stochastic input-to-state stabilization is introduced, and by using this concept a global stabilization controller based on output feedback is constructively designed. (4) For a class of stochastic nonlinear systems with linearly bounded unmeasurable states, the concept of generalized stochastic input-to-state stability is introduced with respect to the noises with unknown covariance and the general stochastic inputs, and by using this concept, output-feedback controllers are constructively designed for stochastic disturbance attenuation and asymptotically global stabilization, respectively. (5) For general stochastic nonlinear systems with time delays, some conditions on the existence and uniqueness of the solution are provided, global (asymptotical) stability in probability is introduced, and the corresponding criterion is obtained. Besides, for a class of uncertain stochastic nonlinear systems with time-varying time delays, an adaptive output-feedback stabilization controller is constructed. |
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| Keywords: | stochastic nonlinear systems zero dynamic inverse dynamic output feedback integrator backstepping method stabilization controller strict-feedback stochastic input-to-state stability |
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