Abstract
此篇論文提出了小波網路的架構去做一個非線性系統的估測，這種小 波網路的節點是由垂直正交的小波基底所 組成，透過參數的 適應調變，我們可由其加權組合得到估測值，此一估測值與實際系統的差 值我們稱之為估計誤差。經由這種小波網路，加上線性化回授控制，此線 性誤差方程式可由我們自行設計，而估計誤差與外界干擾可用 Ｈ∞控制 器以達到估測誤差和外界誤差的衰減效果，因此我們的設計步驟可分成二 個步驟：第一個步驟是由小波網路估測，這可視為是一個粗調的工作，然 後由Ｈ∞控制器去做衰減的微調的工作而去滿我們事先所給定的衰減值。 此衰減值的意義是使干擾對系統的影響在我們衰減值所能控制的範圍內。 我們分別討論單輸入單輸出的系統及多輸入多輸出的系統，在不會造成有 限脫離時間的前提下，我們可由小波網路去設計控制器，參數的調整律及 其演算法則。經由這種強健適應追蹤控制的優點如下：第一，不必事先知 道受控器有沒有傳統適應控制所要求的線性化可分離型式。第二，在暫態 狀態有較快的收斂率。第三，在穩下可保證Ｈ∞的追蹤效能。最後我們由 二個模擬例子去說門這種設計的效能，分別是倒單擺控制和二肘機械手臂 的追蹤控制，在外在干擾的情況下，能達到我們給定的衰減效果。 This thesis proposes an architecture of wave- let network to approximate a nonlinear system. The nodes of such network are composed of the orthnormal wavelet bases. By the adaptive laws of the parameters, we can get the weighted sums of the nodes to approximate the system. By this wavelet network and the linear feedback linearization method, we can design the error dynamic equation. Using the Ｈ∞ controller, the approximation error and the external disturbance can be attenuated by the desired attenuation level. So our design procedure is divided into two steps: the adaptive wavelet control to approximate the nonlinear system and then Ｈ∞ control scheme is specified to attenuate the effect of the approximation error and the external disturbance to meet a desired Ｈ∞ tracking performance. We will discuss the SISO and MIMO systems respectively by the assumption that the approxi- mation eror will not cause the problem of finite escape time. Then we can get the design algorithms of the nonlinear system. The merits of the proposed robust adaptive tracking controlare as follows: (1) the unknown nonlinear plant is not required to be of linear or nonlinear parameterization form as in the con- ventional approaches (2) fast convergent rate at transient state, and (3) the Ｈ∞ tracking per- formance can be guaranteed within some desired le- vel at steady state. Finally, we use two simulation examples to illustrate the proposed design algorithm.