Development of modeling and control analysis of jumpless hybrid systems

无跳混合系统建模和控制分析的开发

• 批准号: 11650449
• 负责人: IMURA Jun-ichi
• 金额: $ 2.37万
• 依托单位: Tokyo Institute of Technology (2001)Hiroshima University (1999-2000)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650449/
• 关键词: hybrid systems; well-posedness; piecewise affine system; stabilization; switch

The purpose of this research project is to develop a series of system control theory from modeling to control for a class of hybrid systems, i.e., piecewise affine systems with no jump phenomena. The result is as follows : first, we have proposed a new concept of discrete transition rule, named switch-based transition rule by regarding the discrete state of the piecewise affine system as 0-1 switches. This rule corresponds to an idealization of switching phenomena with time-delays. Next, we have presented a definition of solutions and well-posedness of such systems, and then a characterization of well-posed systems. This approach gives a basis of the well-posedness analysis even for more general class of hybrid systems. Third, the concept of feedback well-posedness has been proposed and a necessary and sufficient condition for the bimodal system to be rendered well-posed via state feedback, which is a necessary condition for stabilizability. Furthermore, based on this feedback well-posedness analysis, we have derived a canonical form of all feedback well-posed bimodal systems to obtain a sufficient condition for the system to be stabilizable. Finally we have proposed a stabilization method of bimodal systems and 4-modal systems, which shows that the control problem of some class of piecewise affine systems can be reduced to that of the usual linear systems by some feedback transformation.

本研究项目的目的是针对一类混合系统，即无跳跃现象的分段仿射系统，开发一系列从建模到控制的系统控制理论。结果如下：首先，我们将分段仿射系统的离散状态视为0-1个开关，提出了一种新的离散转移规则概念，称为基于开关的转移规则。该规则对应于具有时间延迟的开关现象的理想化。接下来，我们提出了此类系统的解和适定性的定义，然后描述了适定系统的特征。这种方法甚至为更一般类别的混合系统提供了适定性分析的基础。第三，提出了反馈适定性的概念，并提出了双峰系统通过状态反馈达到适定性的充要条件，这是稳定性的必要条件。此外，基于这种反馈适定性分析，我们推导了所有反馈适定双峰系统的规范形式，以获得系统稳定的充分条件。最后我们提出了双模态系统和四模态系统的镇定方法，表明一类分段仿射系统的控制问题可以通过一些反馈变换简化为通常的线性系统的控制问题。

项目成果

井村順一, 清水一寿, 佐伯正美: "2スイッチ駆動ハイブリッドシステムの安定化"システム制御情報学会論文誌. 15巻・3号. (2002)

Junichi Imura、Kazutoshi Shimizu、Masami Saeki：“双开关驱动混合系统的稳定性”，系统、控制和信息工程师学会学报，第 15 卷，第 3 期（2002 年）

J.Imura: "Well-posedness analysis of switch-driven hybrid systems with external inputs"5^<th> IFAC Symposium on Nonlinear Control Systems (NOLCOS). 1521-1526 (2001)

J.Imura：“具有外部输入的开关驱动混合系统的适定性分析”第 5 届 IFAC 非线性控制系统研讨会 (NOLCOS)。

J.Imura, A.J.van der Schaft: "Characterization of well-posedness of piecewise linear systems"IEEE Transaction on Automatic Control. Vol.45,No.9. 1600-1619 (2000)

J.Imura、A.J.van der Schaft：“分段线性系统适定性的表征”IEEE 自动控制汇刊。

J. Imamura and A.J. van der Schaft: "Caracterrization of well-posedness of piecewise linear system"IEEE Transaction on Automatic Control. Vol.45, No.9. 1600-1619 (2000)

J.今村和A.J.

井村順一: "ハイブリッドシステムの制御理論構築を目指して"システム/制御/情報. 43・12. 651-659 (1999)

Junichi Imura：“旨在构建混合系统的控制理论”系统/控制/信息43・12（1999）。