非線性控制系統， 採用“狀態相關(微分形式)Riccati 方程式”設計

Nonlinear control systems, a “state-dependent (differential) Riccati equation ”approach

林立岡(Li-Gang Lin)

指導教授 ： 梁耀文

國立交通大學/電機學院/電機與控制工程系所/博士(2014年)

https://doi.org/10.6842/NCTU.2014.01121

摘要

在非線性控制系統領域，近來提出一種易於實現的控制手法“狀態相關Riccati方程式”，成功應用在許多實際例子上。具備多樣的功能和潛力，並克服一些現存非線性控制手法所無法面對的難題。成功應用的領域包括飛彈、航空載具、衛星、船舶、無人飛行載具、生醫工程系統、工業電子、排程控制、水下載具、和機器人。與他相似的控制手法“狀態相關微分形式Riccati方程式”，近來也引起諸多興趣並被廣泛研究，從理論分析或實際應用等角度上均擁有不錯的潛力，並與“狀態相關Riccati方程式”控制手法共享諸多設計上的優點，差別主要在於考慮的時間範圍(“狀態相關Riccati方程式”考慮無限時間範圍；“狀態相關微分形式Riccati方程式”考慮有限時間範圍)。然而，針對此兩種新穎的控制手法，目前尚十分缺乏嚴謹紮實的理論基礎，來支持諸多的實際應用，特別是所擁有的設計自由度(狀態相關係數矩陣的不唯一性)，及其如何影響系統的表現，等都是學者專家關心且積極研究的課題。在這篇博士論文中，考慮一般階數非線性時變系統，諸多與此設計自由度相關的重要議題將被探討並提出可行的解決辦法，在初期控制器設計上將扮演關鍵角色。最後，所提出的結果將與文獻上諸多不同主題的貢獻相互參照，試圖找出關聯性和相似性。最後，透過許多代表性的例子(包括現實生活中的實際應用)模擬所提出的結果，佐證結果的正確性和可行性。

關鍵字

狀態相關(微分形式)Riccati方程式 ； 非線性控制系統 ； 狀態相關係數矩陣

並列摘要

In the area of nonlinear control systems, recently the easy-to-implement state-dependent
Riccati equation (SDRE) strategy has been shown to be effective by numerous practical
applications, possessing collectively many of the capabilities and overcoming many of the
difficulties of other nonlinear control methods. Its diverse fields of applications include
missiles, aircrafts, satellites, ships, unmanned aerial vehicles (UAV), biomedical systems
analysis, industrial electronics, process control, autonomous maneuver of underwater vehicles,
and robotics. Due to the great similarity to SDRE, the newly emerged state-dependent
differential Riccati equation (SDDRE) approach exhibits great potential from both the
analytical and practical viewpoints, and shares most of the benefits of SDRE while differing
mainly in the time horizon considered (i.e. finite for SDDRE and infinite for SDRE).
However, there is a significant lack of theoretical fundamentals to support all the successful
implementations, especially the feasible choice of the possessed design flexibility (namely,
iv
the infinitely many factorizations of the state-dependent coefficient matrix) with predictable
performance is still under development for both schemes. In this thesis, considering the
general finite-order nonlinear time-variant systems, several problems related to the design
flexibility are investigated and solved, which appear at the very beginning of the
implementation of both schemes. Finally, connections to the literature in various topics of
research are established, and the proposed scheme is demonstrated via examples, including
real-world applications.

並列關鍵字

State-dependent (differential) Riccati equation ； nonlinear control system ； state-dependent coefficient matrix

參考文獻

16 May 2000.

attitude control of a satellite using the state-dependent riccati equation

determination and control system via magnetic measurements and

actuation. Acta Astronautica 69 (2011), 168–185.

[7] Afanas’ev, V. N. Control of nonlinear plants with state-dependent