| 摘要: | 非嚴格反饋系統的控制問題，近年來成為相關學術界及業界注目的焦點。現有多數的適應性控制方案，由於所採用的參數更新律中只包含追跡誤差而無納入辨識誤差，因此雖然可達到最終追跡準確性，但相關辨識結果往往不盡理想，導致較差的追跡暫態響應。可以預期的，當未知函數被辨識的越準確其追蹤軌跡效果越佳。有鑒於此，本計畫擬針對非嚴格反饋系統，提出一結合所謂之浸入式參數更新律的適應性類神經控制設計，以同時達到追跡與未知函數線上辨識的雙重目的。計畫初期將先對可線性化系統做探討，此類系統的狀態微分可直接取得，明顯地簡化了理論分析與設計。以此成果為基礎，接著將其推廣至非反饋系統。相較於可線性化系統，此部分主要困難在於系統狀態的微分無法量測，需建構適當狀態濾波器以估測該微分項，產生的近似誤差不確定性則以動態調整方式以及調整濾波器增益加以克服。最後在理論設計完成後，本計畫擬將所發展設計應用於磁浮定位系統，以驗證其有效性。本計畫的完成將做出以下主要貢獻: 1) 浸入式參數更新律近年來已被廣泛應用於控制系統的理論設計或實際應用，然而截至目前為止，此種方案只限於控制係數函數為已知且系統不存在非結構不確定性的情況，本計畫則針對這兩項限制提出解決方案; 2) 浸入式設計的有效性前提是控制律與參數更新律需具有相同之估測誤差，然而針對非嚴格反饋系統的控制問題，現有文獻上廣被採用的變數分離法需對集成未知函數加以近似補償，並不適用。相對而言，以107學年度科技部研究成果為基礎，本計畫發展的方案可在每一設計步驟中直接對系統未知函數做估測補償，有效解決上述困難。
Control of nonstrict-feedback systems has attracted much attention in both the academic and industrial fields in recent years. However, most existing schemes, despite their ability in attaining the tracking objectives, the adopted parametric update algorithms are built based on the tracking errors instead of the estimation errors. Accordingly, they do not ensure the identification of the unknown nonlinearities in general, which leads to unsatisfactory transient tracking performances consequently. As can be expected, higher identification accuracy leads to better tracking performances in practice. Regarding this, this project aims to develop an Immersion and Invariance (I&I) based adaptive neural control algorithm, aiming to attain the objectives of tracking and on-line identification simultaneously. The project will be started from the simpler linearisable systems, for their states’ derivatives can be readily obtained, rendering the corresponding theoretical analysis and control design easier. Next, the project will turn to the more complex nonstrict-feedback systems. Comparing with the linearisable systems, the major difficulty in such cases is that the derivatives of the states are not available. It will be resolved via constructing adequate state filters. The inevitable estimation errors will be tackled with via dynamic scaling and the adjustment of the gains in the filter dynamics. Finally, the developed control algorithms will be applied to a magnetic levitation system for demonstrating their validity. The contributions of this project are summarized as follows i) The I&I method has been widely applied to the theoretical control designs and practical applications in recent years, however, they are restricted to cases with known control-affine functions and without the presence of unstructured uncertainties. The developed schemes relax these two restrictions. ii) The prerequisite of the I&I approach is the estimation errors appearing in the control and the update algorithms should have the same form. Noticeably, the common variable-separation approach uses the neural networks for approximating the packed unknown nonlinearities instead of the original ones, which prohibits the application of the I&I method. In contrast, based on the achievement of our project in the 107 academic year sponsored by MOST, the developed scheme in this project allows us to compensate the unknown nonlinearities directly in each design step. The aforementioned demand is fulfilled as a consequence. |
