臺灣博碩士論文加值系統

在本論文中，新建立了一個適用於多變殊異擾動系統的線性二次納許賽局追蹤器。加入LQR設計方法應用於追蹤器設計的兩個二次估測方程的常態交錯多變數立卡迪函數(GCMARE)需要被解出。首先，新提出了針對GCMARE的漸進擴展式，且提出基於牛頓法的演算法來解GCMARE且保證其收斂性。然後，藉由數位再設計的方法設計出一個低增益且有高效能的控制器。最後，為了增進追蹤器的效能，使用了渾沌進化演算法(CEPA)來調整追蹤器的參數。最後以一個例子來驗證提出的方法是有效的。

In this thesis, a tracker for the linear quadratic Nash game of multiparameter singularly perturbed sampled-data systems is newly established. A generalized cross-coupled multiparameter algebraic Riccati equation (GCMARE) for two quadratic cost functions is needed to be solved by applying the LQR design methodology for the tracker design. Firstly, the asymptotic expansions for the GCMARE are newly established, and the proposed algorithm based on the Newton’s method for solving the GCMARE guarantees the quadratic convergence. Then the low-gain sample-data controller with a high design performance is realized though the digital redesign method. Finally, for further improving the tracking performance, the chaos evolutionary programming algorithm (CEPA) is utilized to tune the parameters of the tracker. An example is presented to demonstrate the effectiveness on the proposed methodology

List of Contents
Page
Chinese Abstract............................................... I
Abstract ..............................................................II
Acknowledgments .......................................................III
List of Contents.......................................................IV
List of Tables ........................................................V
List of Figures .......................................................VI
Content
Chapter 1 Introduction ................................................1-1
Chapter 2 Linear Quadratic Nash Game Based Tracker for Multiparameter Singularly Perturbed Sampled-data Systems： Digital Redesign
Approach................................................................2-1
2.1 The design of controller with digital redesign method .........2-2
2.1.1 Digital redesign approach..................................... 2-2
2.1.2 The matrix sign function.......................................2-9
2.1.3 Asymptotic structure ..........................................2-11
2.1.4 Newton’s method ..............................................2-17
2.2 The chaos-evolutionary-programming approach ...................2-23
2.2.1 The chaos system selected for optimization ....................2-23
2.2.2 The chaos-evolutionary-programming approach ...................2-23
2.3 An illustrative example........................................2-29
Chapter 3 Conclusion....................................................3-1
References .............................................................R-1
Appendix................................................................A-1

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