雖然上一年的國科會計畫完成了對嚴格回授系統(strict-feedback system)的全域適 應性類神經控制設計，然相關之參數爆炸(explosion of learning parameters)及控制器複 雜性爆炸問題(explosion of complexity)仍未解決。參考數種現有方法，由於最小學習參 數法(minimal learning parameters)所需估測參數最少，因此本計畫擬採用此法來解決參數 爆炸問題。至於控制器複雜性爆炸，主要指回步設計中需重複將虛擬控制輸入的微分 項消去，造成最終實際控制律過於複雜的問題。此問題等同於如何有效避免對虛擬虛 擬輸入的直接微分。目前廣被採用的是所謂的動態曲面控制法(dynamic surface control)，主要是以濾波器輸出取代虛擬輸入，並以濾波器輸出的微分取代虛擬輸入的 微分的方式，降低控制器的複雜性。針對此問題，本計畫擬同時採用高增益觀測器及 動態曲面控制法於全域控制設計中，並比較其優劣。最後，因全域穩定的緣故，本計 畫的成果預計可免除半全域的控制設計對系統初值的許多限制，因此也更具實用性。 Although the adaptive neural controller in our last project has achieved global tracking stability for strict-feedback systems, however, the corresponding explosion of learning parameters and explosion of complexity have not yet been tackled so far. Among others, the method of minimal learning parameters is most efficient and hence will be adopted here for dealing with the first problem mentioned above. On the other hand, it is known that the explosion of complexity arises from the repetitive differentiation of the virtual controller in the backstepping design step and the subsequent cancellation. So solving such a problem means to avoid the direct differentiation of the virtual controllers. The so-called dynamic surface control has become the major tool to that end in recent years. It mainly involves a set of first-order filters with the virtual controllers as the inputs, and whose outputs are used in place of the virtual controllers in the cancellation procedures. Differentiation of the virtual controllers is now replaced with the differentiation of the outputs of the filters and hence the explosion of complexity is avoided under such circumstances. In this project, we intend to use both the high-gain state observers and the dynamic surface control to tackle this problem and then compare their properties. Finally, by virtue of the global stability, the restriction on the initial states of the system in the existing semi-global approaches is expected to be lifted in our scheme. It hence is more attractive to the practical applications.
