以小波基底函數為基礎的適應性倒階控制應用於具有驅動飽和限制之不確定系統

Abstract

本篇論文提出三種非線性系統的控制方法。首先，在第二章先提出一個小波基底函數適應性倒階典型非線性系統的控制器。本文提出小波類神經自適應倒階控制器來控制未知的非線性系統。這個控制器結合小波基底函數與驅動飽和限制。接著，在第三章提出一個小波基底函數適應性倒階非典型非線性系統的控制器。本文中推薦在非典型非線性系統使用小波適應性倒階去控制。此控制方法結合適應性倒階控制器及小波基底函數，並以此方法近似未知的動態系統，小波基底函數擁有良好的近似性能，它較適合線上動態系統藉由調整內部的參數，以均值定理設計參數適應律來避免基底微分，且使用濾波器在控制輸入上減少基底微分計算量。最後，本篇論文提出結合小波適應性倒階與一階濾波器的設計概念來控制非典型非線性系統。而系統的穩定性以李亞普諾夫函數方程式分析說明，再以電腦舉例模擬論證本文所提出方法之控制性能與應用性。Three control methods for nonlinear systems are proposed in this study. The first controller design is about a wavelet adaptive backstepping controller for affine nonlinear systems. The controller is comprised of a wavelet identifier and actuator saturation. The second controller design is about a wavelet adaptive backstepping controller for nonaffine nonlinear systems. A wavelet adaptive backstepping controller for a nonaffine system is proposed in this paper. The control scheme combines the backstepping technique and adaptive control with wavelet function. The wavelet function has well performance. It is much proper to online compute the system dynamics by tuning its interior parameters. A mean-value estimation method is also proposed to avoid a higher-order derivative problem generated by Taylor linearization expansion.The third controller design is about a wavelet adaptive backstepping controller for nonaffine nonlinear systems with first order filters. Furthermore, the stability of the system with the mean-value theorem is dissected through Lyapunov functions. In the end, simulation results illustrate the application of the proposed scheme.