整合SDRE和ISMC設計之非線性系統可靠度控制理論與應用

Abstract

本論文探討非線性系統使用state-dependent Riccati equation (SDRE)理論的可靠度控制設計，並應用於衛星之姿態控制。由於引進了integral sliding mode control (ISMC)理論合併使用，研究發現可以大大增進系統的穩健性和可靠度。然而，傳統的SDRE設計必須先拆解漂流項成為f(x)=A(x)x的形式，然後再利用A(x)及線性理論來判斷系統在該狀態的可穩定性和可觀測性以確保對應之SDRE存在正定解。但當系統動態足夠複雜時，這些判斷條件不容易被檢驗，此外，目前文獻也沒有提供不同拆解方式的分析與比較。因此，本論文提出另一種SDRE的拆解方式，並探討能保證對應的Riccati方程式存在正定唯一解的充分且必要條件，此充要條件只需要系統動態在該狀態之資訊。本論文中也發現如果採用固定拆解方式的傳統SDRE設計方法能夠正常工作，那麼本論文探討的SDRE拆解方式一樣可以正常工作。透過例子，我們說明了本論文提出拆解方法的好處。

In this thesis, we investigate the nonlinear reliable control issues via the state-dependent Riccati equation (SDRE) scheme with application to the attitude control of a satellite. Owing to incorporating with the integral sliding mode control (ISMC) design, both the robustness and the reliability performances are greatly improved. However, it is known that the conventional SDRE scheme has to symbolically factorize the drift term in the form of f(x)=A(x)x, and then using this A(x) to check system's stabilizability and observability symbolically at every nonzero state for ensuring the solvability of an associated SDRE. These checking conditions are in general not easy to implement when the system dynamics is complicated, and there is no guideline provided for performing the factorization. As a result, this study also presents an alternative approach of factorization, which only requires the information of the system dynamics at every state and guarantees the existence of a unique positive definite solution of the associated Riccati equation when a mild condition is satisfied. It is shown that the alternative approach always works if the conventional SDRE approach adopting any specific factorization for f(x) is successfully operated. An illustrative example is also given to demonstrate the benefits of the alternative approach of factorization.