線性時變系統的範數模式和相關控制設計

A Two-Norm Model of Linear Time-Varying System and Related Control Designs

張明新(Ming-Hsing Chang)

指導教授 ： 陳明新

國立臺灣大學/工學院/機械工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00325

摘要

在本篇論文中，我們要介紹一個非線性狀態轉換來將一個線性時變系統轉換到一個純量系統，並且探討該純量系統在控制輸入下的狀態變化。接著，利用不同的控制方法來針對這個純量模式加以控制，控制的方法包括forward Riccati equation control、controllability grammian control、least square control以及division control共四種。然而，在控制的過程中，即使線性時變系統是可控制的，該純量系統有可能會失去可控制性。因此，這是未來還需要研究的課題。

關鍵字

division control ； 線性時變系統 ； least square ； controllability grammian ； forward Riccati equation

並列摘要

In this thesis, we introduce a nonlinear state transformation to transform a linear time-varying system into a scalar system, which describes how the two-norm of the system state changes with the control input. With this two-norm scalar model, different control designs can be constructed, including the forward Riccati equation control, controllability grammian control, least-squares control, and the division control. However, even if the linear time-varying system is controllable, the two-norm
scalar system may lose its controllability in the process of control. Hence, further research is required in the future.

並列關鍵字

controllability grammian ； least square ； linear time-varying system ； division control ； forward Riccati equation

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