- 學位論文
具邊界未知時變不確定性之非線性系統的適應性控制：函數估測法
Adaptive Controller for Nonlinear System with Unknown Time Varying Uncertainty Bound: Function Estimation Approach
摘要
利用適應性控制法來克服系統參數不確定性的問題在控制領域是很常見的，藉由設計一個參數調整演算法來達到即時估測不確定性參數，進而穩定整個閉迴路系統。但由於一般不確定性具有時變的特性且其變動範圍亦為未知，故傳統之適應性控制與強健控制通常無法直接使用。 近年來函數估測技術廣泛使用於具一般不確定性非線性系統的適應控制。該技術主要將不確定性參數轉換為有限的基底函數(正交函數或神經元)與未知係數的組合，並設計未知係數的參數估測器使全系統穩定。其中有兩種廣為人知的函數估測器分別為：類神經網路與正交級數。然而在實際應用函數估測器上仍存在一些問題，如奇異值問題。此問題通常發生在估測系統的未知輸入增益，奇異值的發生可能會造成整個控制系統的發散。 本論文的重心將放在正交級數的函數估測器上，提出以哈爾小波維基礎的適應性滑動控制器。本研究中所有時變參數均假設為未知，且考慮其變化範圍亦為未知時的控制器之設計。既然系統的參數具有時變性質，故本研究將採用函數估測的技術來克服此問題。然而如同大多數以函數估測為基礎之適應性控制器，奇異值問題亦會發生於輸入增益函數的估測過程，這將會造成控制信號的發散。本研究所提出的控制器均可利用Lyapunov穩定理論證明其穩定性，且奇異值問題亦可被克服，並利用電腦模擬來驗證其可行性。
並列摘要
Using adaptive control theory to conquer uncertainty problem of system is common on control sites. The main idea is to use parameter adjust algorithm to estimate unknown parameters, and stabilize overall closed loop system. However, general uncertainties have characteristics of time-varying and unavailable variation bounds, such that traditional adaptive control laws or robust schemes can not be directly used. In recent stage, function estimation approaches have been widely applied on uncertain nonlinear system. The concepts of these techniques are to transform the uncertain parameters to finite combination of basis functions (neurons or orthogonal basis functions) with unknown coefficients. The unknown parameters update laws can be obtained by using Lyapunov stability theory. Moreover, overall system stability can also be guaranteed. There are two well known function estimators: neural network and orthogonal series. In practical, there are still remaining some problems while using these approaches, such as singularity problem. The singularity problem often occur during the procedure of unknown input gain estimation, which may cause the control effort to become unbounded. This dissertation aims to develop an non-singularity adaptive controller based on Haar wavelet function estimator. In this research, system uncertainties are assumed to be time varying with unknown variation bounds. Parameters adaptive laws and overall system stability can be obtained by using Lyapunov theory. Furthermore, the singularity problem can also be solved by proposed control strategy. The experimental result of computer simulation was used to verify the validity and effectiveness of the proposed control law.