| 摘要: | 非線性系統觀察器和控制器的設計被研究人員認為是一個巨大挑戰。一般而言，一個非線性系統擁有複雜的組成，觀察器和控制器設計可能會很困難。因此，將非線性系統轉換為其他模型是必要的。在本研究中，非線性系統被轉換成四個模型，分別是離散時間不確定性T-S模糊模型，不確定性多項式模型，不確定性多項式T-S模糊模型和具有擾動的連續時間T-S模糊系統。然後將觀察器和控制器合成到這些系統模型用於代替原來的非線性系統。本文中觀察器被合成用於對離散時間不確定性T-S模糊系統、不確定性多項式T-S模糊系統研究;而針對具有擾動的連續T-S模糊系統和不確定性多項式系統，設計了基於觀察器的控制器。值得注意到的是隨著不確定性和擾動的存在，非線性系統的觀察者和控制器的合成變得更加困難。因為不確定性/擾動總是使估計誤差和狀態無法漸近收斂為零。
在這篇論文中，我們的貢獻被提出在四個主要章節。在第3章，一種基於未知輸入的新方法被提出，合成的觀察器用於去估計離散時間不確定性T-S模糊系統的不可測狀態變數。這種新方法不僅可以消除不確定性的影響，還可以使估計狀態在未知不確定性上限的情況下漸近地接近真實狀態。此外，前件部變數依懶和獨立與不可測量的狀態變數被用於研究離散時間不確定性T-S模糊系統。此外，非常用的二次項Lyapunov函數被用來使觀察器設計的條件更加寬鬆。在第4章，一個新方法被提出來用於設計不確定性多項式T-S模糊系統的觀察器，不確定性上限不會被提前給出。一種新的多項式觀察器形式被提出，在沒有設計控制器和不知道不確定性上限的情況下去估計非可測狀態，並完全地消除不確定性的影響。此外，利用非常用的Lyapunov函數和SOS技術，推導出了觀察器合成的充分條件。
在第5章中介紹了一種用於合成基於觀察器的不確定性多項式系統控制器的新方法。不確定性多項式系統被轉化為具有擾動的多項式系統，然後，為該系統設計了基於觀察器的控制器。基於未知輸入的新的控制過程被提出去估計狀態和穩定系統當在不確定性上限和所有或者某些狀態的上限是未知的情況下。另外，一個新的觀察器架構被合成去同時地估計不可測狀態和擾動。在第6章，基於觀察器的控制器被合成到有擾動出現的連續T-S模糊系統。擾動的種類極大地擴大了，因為它不需要滿足嚴格的約束條件，如有界的、有限的導數等於零或由外生模型生成。一種新的狀態和擾動觀察器被提出用於估計不可測狀態和擾動，該控制器與狀態和擾動觀察器結合在一起是為了消除擾動的影響穩定系統。
總之，本文提出了一些方法為不確定性非線性系統合成觀察器和控制器。根據Lyapuov理論，依據LMIs（線性矩陣不等式）和SOS（平方和），在Matlab中用LMIs工具和SOS工具來解決問題，推導出觀察器和控制器的設計條件。最後舉例說明了所提出的方法的有效性和優越性
;Observer and controller design for nonlinear systems is categorized as a great challenge for researchers. In general, because a nonlinear system may have a complex form, observer and controller design may be difficult. Therefore, transforming the nonlinear system into other models is always necessary. In this study, the nonlinear system is transformed into four models which are the discrete time uncertain T-S fuzzy model, uncertain polynomial model, uncertain polynomial T-S fuzzy model and continuous time T-S fuzzy system with the disturbance, then the observer and controller are synthesized for these system models instead of the original nonlinear systems. Particularly, in this dissertation, the observer is synthesized for the discrete time uncertain T-S fuzzy systems, uncertain polynomial T-S fuzzy system; and the observer-based controller is designed for the continuous T-S fuzzy systems with disturbances and the uncertain polynomial systems. It is noted that with the existing of the uncertainties and disturbances, synthesizing the observer and controller for the nonlinear systems becomes much more difficult. Because the uncertainties/disturbances always make the estimation errors and the states be unable to converge zero asymptotically.
In this dissertation, the contributions are presented in four main chapters. In Chapter 3, a new methodology based on the unknown input method is proposed for synthesizing the observer to estimate the un-measurable state variables of the discrete time uncertain T-S fuzzy system. This new approach allows us not only eliminate the effects of uncertainties but also make the estimated states approach to real states asymptotically without knowing the upper bounds of the uncertainties. Moreover, both premise variables are dependent and independent on the unmeasured state variables are investigated for the discrete time uncertain T-S fuzzy system. Additionally, the non-common quadratic Lyapunov function is employed to make the conditions for the observer design be more relaxed. In Chapter 4, a new approach to design the observer for uncertain polynomial T-S fuzzy system is proposed. The upper bounds of the uncertainties are not given in advance. A novel polynomial observer form is proposed to estimate the un-measurable states and eliminate completely the influences of the uncertainties without designing a controller and knowing the upper bounds of the uncertainties. Moreover, with the aids of the non-common Lyapunov function and SOS technique, the sufficient conditions for observer synthesis are derived.
Furthermore, new methodology to synthesize the observer-based controller for the uncertain polynomial system is established in Chapter 5. The uncertain polynomial system is transformed into the polynomial system with the disturbance then the observer-based controller is designed for this system. The novel control process based on the unknown input method is proposed to estimate states and stabilize the system in which the upper bounds of uncertainties and all/some states are unknown. Besides, a new framework of the observer is synthesized to estimate the un-measurable states and the disturbances simultaneously. In Chapter 6, the observer-based controller is synthesized to the continuous T-S fuzzy system with the presence of the disturbance. The class of the disturbance is significantly enlarged because it does not need to satisfy the strict constraints such as bounded, finite derivative is equal to zero or generated from the exogenous model. A new form of the state and disturbance observer is proposed to estimate the unmeasurable states and disturbance simultaneously. The controller incorporating with the state and disturbance observer is designed to counteract to the impacts of the disturbance and stabilize the system.
In conclusion, this dissertation proposed several methods to synthesize observer and controller for the uncertain nonlinear system. On the basis of Lyapuov theory, the conditions of design observer and controller are derived in term of LMIs (Linear Matrix Inequalities) and SOS (Sum of Squares) which can be solved by LMIs tool and SOS tools in Matlab. Finally, several examples are shown to illustrate the effectiveness and advantages of the proposed methods. |
