A study on the construction of a framework of control theory based on organic combination of algebraic and analytic methods

代数与解析方法有机结合的控制理论框架构建研究

• 批准号: 12650444
• 负责人: HAGIWARA Tomomichi
• 金额: $ 2.18万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12650444/
• 关键词: sampled-data systems; linear periodic systems; frequency response operator; positive-realness; Nyquist stability criterion; spectral analysis; harmonic Lyapunov equation; bisection method; ロバスト安定解析; 物理パラメータの不確かさ; 一般化固有値問題; 制御装置の離散化; サンプル値系; 周

This research aims at constructing a new framework for design and analysis of control systems in such a way that algebraic and analytic methods are combined in an organic fashion. Here, an algebraic method includes such approaches involving eigenvalue/eigenvector analysis of matrices. spectral analysis of operators and determinant theory of matrices and operators. On the other hand, an analytic method includes such approaches involving functional analysis, operator theory and complex function theory. In this research design and analysis of sampled-data systems as well as analysis of linear continuous-time periodic systems are particularly focused on.In the study of sampled-data systems, efficient and fairly accurate upper and lower bounds for the frequency response gain are derived, and a bisection method to compute the exact frequency response gain to any degree of accuracy from those upper and lower bounds is also established, including associated computer programs. Also, positive-re … More alness and Nyquist stability criterion are studied, and spectral properties of operators associated with sampled-data systems are clarified.In the study of linear continuous-time periodic systems, we first dealt with the associated frequency response operator, which plays a key role in the study of linear continuous-time periodic systems, and clarified the conditions that should be satisfied by the system so that the associated frequency response operator can be defined in a rigorous fashion. Furthermore, properties of the frequency response operators are studied thoroughly, by which a solid basis has been established for studies to follow. These results are extended to enable us to analyze stability of linear continuous-time periodic systems through an infinite-dimensional algebraic equation which we call a harmonic Lyapunov equation. Effectiveness of the analysis using this equation is shown, and it is also shown that the H2 and H-infinity performance analysis can be carried out through what we call skew truncation of infinite-dimensional matrices. Convergence properties regarding this truncation are also established. Less

本研究旨在构建一个新的控制系统设计和分析框架，将代数方法和解析方法有机地结合起来。这里，代数方法包括涉及矩阵的特征值/特征向量分析的方法。算子的谱分析以及矩阵和算子的行列式理论。另一方面，解析方法包括泛函分析、算子理论和复变函数理论等方法。在本研究中，特别关注采样数据系统的设计和分析以及线性连续时间周期系统的分析。在采样数据系统的研究中，推导了有效且相当准确的频率响应增益的上限和下限，并建立了从这些上限和下限计算任意精度的精确频率响应增益的二分法，包括相关的计算机程序。还研究了正响应和奈奎斯特稳定性判据，明确了与采样数据系统相关的算子的谱特性。在线性连续时间周期系统的研究中，我们首先讨论了相关频率响应算子，它在线性连续时间周期系统的研究中起着关键作用，并明确了系统应满足的条件，以便可以严格地定义相关频率响应算子。此外，还对频率响应算子的性质进行了深入的研究，为后续的研究奠定了坚实的基础。这些结果经过扩展，使我们能够通过无限维代数方程（我们称之为调和李亚普诺夫方程）来分析线性连续时间周期系统的稳定性。显示了使用该方程进行分析的有效性，并且还表明可以通过我们所说的无限维矩阵的斜截断来进行 H2 和 H-无穷大性能分析。还建立了关于该截断的收敛性质。较少的

项目成果

J.Zhou, T.Hagiwara: "H2 and H∞ Norm Computation of Linear Continuous-Time Periodic Systems Via the Skev Analysis of Frequency Response Operators"Automatica. 38・8. 1381-1387 (2002)

J.Zhou，T.Hagiwara：“通过频率响应算子的 Skev 分析进行线性连续时间周期系统的 H2 和 H∞ 范数计算”Automatica 1381-1387。

Y.Ito, T.Hagiwara, H.Maeda, M.Araki: "Time-Sharing Multirate Sample-Hold Controllers and Their Application to Reliable Stabilization"Dynamics of Continuous, Discrete and Impulsive Systems Series B : Applications & Algorithms. 8・4. 445-463 (2001)

Y.Ito、T.Hagiwara、H.Maeda、M.Araki：“分时多速率采样保持控制器及其在可靠稳定中的应用”连续、离散和脉冲系统动力学 B 系列：应用与算法 8・4。 .445-463 (2001)

T.Hagiwara, M.Suyama, M.Araki: "Upper and Lower Bounds of the Frequency Response Gain of Sampled-Data Systems"Automatica. 37・9. 1363-1370 (2001)

T.Hagiwara、M.Suyama、M.Araki：“采样数据系统的频率响应增益的上限和下限”Automatica 37・9（2001）。

T. Hagiwara: "Spectral Analysis and Singular Value Computations of the Noncompact Frequency Response and Compression Operators in Sampled-Data Systems"SIAM Journal on Control and Optimization. Vol.41, No.5. 1350-1371 (2002)

T. Hagiwara：“采样数据系统中非紧频率响应和压缩算子的频谱分析和奇异值计算”SIAM 控制与优化杂志。

J. Zhou, T. Hagiwara, M. Araki: "Stability Analysis of Confinuous-Time Periodic Systems via the Harmonic Analysis"IEEE Transactions on Automatic Control. Vol.47, No.2. 292-298 (2002)

J. Zhou、T. Hagiwara、M. Araki：“通过谐波分析进行连续时间周期系统的稳定性分析”IEEE 自动控制汇刊。