臺灣博碩士論文加值系統

本論文主要是在探討最佳$L^{\infty}$模式簡化的問題。在頻率領域下，
這個問題被轉換成最佳參數的搜尋問題。為了獲得問題的全域最佳解（
global optimal solution），吾人提出一種以基因演算法為工具的強韌
搜尋機制。在穩定性的要求之下，關於搜尋最佳簡化模式係數之最大困難
，是在於可行解的區間通常不是凸集合，而且無法簡單地描述出區間的邊
界。應用Routh穩定性參數的特性，可避免隨時監控簡化模式之穩定性。
然而，無界的Routh穩定性參數區間並不適合使用基因演算法求得全域最
佳的$L^{\infty}$簡化模式。在此，吾人提出另外一種更為良好的方法使
得基因演算法能夠有效地搜尋出最佳簡化模式。此方法的三個主要特點是
：（1）基因演算法的參數搜尋空間是有界的；（2）簡化模式保留了原始
模式的穩定性，以及有限和無限零點的結構；（3）基因演算法解的精確
度可以大為提昇。藉著以Schur與anti-Schur多項式表示簡化模式，前兩
點特性便得已達成；而（3）是由吾人在此提出的新基因演算法運算子：
「區間收縮機制」所獲得。而這種GAs搜尋方法，吾人業已成功地運用至
single-input-single-output（SISO）系統與不穩定系統含有非最小相位
（nonminimum-phase）的模式簡化工作上。此外，對於二維bounded-
input-bounded-output（BIBO）穩定系統的轉移函數之簡化工作方面，我
們亦是利用GA搜尋Schur參數組，以建構出最佳$H^{\infty}$-norm的二維
separable-dominator system（SDS）之簡化模式。

In this thesis, the optimal $L^{\infty}$ model reduction
problemis addressed. In the frequency domain setting, the
problem is formulated asan optimal parameter selection problem.
In order to obtain the global optimalsolution to the
$L^{\infty}$ model reduction problem, a robust search schemeof
using genetic algorithms (GAs) is proposed.Under the stability
constraints, the major difficulty associated withthe search of
optimal coefficients for a reduced-order model lies inthe fact
that the feasible coefficient domain is in general not convex,
andthat the domain boundary cannot be simply described. To avoid
monitoringthe stability in the process of searching reduced-
order models,the Routh stability parameters of a reduced-order
model are often chosenas the decision parameters.However, the
unbounded domain of the Routh $\gamma$- parameters is not
suitablefor obtaining the true global solution tothe optimal
$L^{\infty}$ reduction problem by GAs.A more superior approach
is presented in this thesis to facilitate the use of GAsfor
searching effectively for optimalreduced-order models.The
prosposed approach has the following three distinct features:(1)
the parameter space for GA search is bounded; (2) the finite and
infinitezero structures as well as the stability of the original
system are retainedin the reduced-order model; and (3) the GA
solution accuracy can be greatly enchanced.The first two
features are achieved through representing a reduced-order model
ina transfer function parametrized in terms ofSchur and anti-
Schur polynomials, whereas the third feature is gained byusing a
region contration scheme.The proposed GA search methods are
successfully applied to optimalmodel reduction for single-input-
single-output (SISO) systems andunstable systems with
nonminimum-phase.Besides, the problem of computing optimal
$H^{\infty}$separable-dominator system (SDS) reduced modelfor a
2-D bounded-input-bounded-ouput (BIBO) stable system described
byits transfer function is also solved here through searching
for the optimalSchur parameters of the 2-D SDS reduced-order
model by GAs.