本篇論文提出三種非線性系統的控制方法。首先，在第一章先提出一個B-spline適應性倒階典型非線性系統的控制器。這個控制器結合B-spline類神經近似器與強建控制器。主要控制器為B-spline類神經近似器而強建控制器符合 的追蹤效能。B-spline類神經再局部調整的能力比其他類神經來的優異許多，所以非常適合透過內部參數(控制點或是結點)的訓練來即時估測未知的動態系統，為了及時調整這些參數，本篇論文提出均值定理來取代泰勒級數展開的方式避免B-spline基底高次項微分的問題。在第二章我們提出一個B-spline適應性倒階非典型非線性系統的控制器。這個控制系統包含B-spline均值估測類神經網路倒階控制系統設計，而此系統利用均值的觀念來設計即時的更新律。最後，本篇論文提出結合B-spline適應性倒階與一階濾波器得設計概念來控制非典型非線性系統。在n階到階設系統設計的過程中都會發生運算量激增的問題，所以為了克服這問題在本章再傳統到階設計時的每一階步驟都引入一階濾波器的觀念來解決這類問題。

Three control methods for nonlinear systems are proposed in this thesis. The first controller design is about a B-spline adaptive backstepping controller for affine nonlinear systems. The controller is comprised of a B-spline neural network identifier and a robust controller. The B-spline neural network identifier is the main controller and the robust controller is developed to achieve tracking performance to a desired attenuation level. B-spline neural networks have the advantage over other neural networks of local output adjustment, allowing them to more easily online estimate the system dynamics by tuning their interior parameters, including control points and knot points. To online adjust these parameters, a mean-value estimation technique is proposed to avoid the higher-order derivative problem. This problem generated by both the Taylor linearization expansion and the requirement of finding the derivatives of B-spline basis functions with respect to their parameters. The second controller design is about a B-spline adaptive backstepping controller for nonaffine nonlinear systems. The control scheme combines the backstepping design technique with mean-estimation B-spline neural networks. The mean-estimation B-spline neural networks use a mean estimation technique to develop the update laws for the design of online adaptive controllers. The third controller design is about a B-spline adaptive backstepping controller for nonaffine nonlinear systems with first order filters. The backstepping design technique suffers from on explosion of complexity as order of system increases. In order to overcome this problem, the third controller design uses first order filter at each step of the backstepping design.

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