本篇論文主要著重於滿足單邊利普希茨以及二次內積有界範疇之多代理人系統。利普希茨類非線性系統即屬於此類之特例. 本研究首先設計一個完全分佈之共識協定，其完全分佈即代表動態耦合增益。其次，再設計一個容錯共識協定。兩種協定均屬於無向式通信協議之觀測接收器設計方式。由於考量非線性之特性，共識協定之設計係採用線性矩陣不等式。觀測器增益之設計則採用奇異點分解技術。容錯共識協定設計，係假設執行器具有部分失效以及相關之附加非線性。由於兩項共識協定設計於系統線性部分皆考慮了有限界之外部干擾及不確定性，故達到了容錯共識協定之穩健性。最後，於考量偏差循環追蹤協定之前提下，採取單一集成代理形式，故圖形乃具備有向性。由於循環追踪協定之旋轉角所導致之穩定性問題，故本研究添加額外之非線性函數處理。值得注意的是，本研究所應用之非線性函數屬於Hopf振盪器動力學，其亦滿足單邊以及二次內界之條件。龐加萊映射(Poincare map)通常用於顯示準週期軌跡之存在。所有設計皆已透過數值模擬進行驗證。

This dissertation focuses on a class of multi-agent system that satisfies criteria of one-sided Lipschitz and quadratic-inner boundedness. First, a fully distributed consensus protocol is designed for the unceratin multi-agent system. Fully distributed here implies a dynamic coupling gain. Next, a fault-tolerant consensus protocol is designed. The consensus protocols employs an observer-based design and the communication protocol is undirected. To account for nonlinearity, the consensus protocol is designed by using linear matrix inequalities technique. To design the observer gain, singular value decomposition technique is utilized. For the fault-tolerant consensus protocol design the actuators are assumed to have partial loss of effectiveness and an associated additive nonlinearity. Moreover, both the designs considers bounded external disturbances and uncertainties in the linear part of the system, hence the protocol is robust. Finally, formation of single integrator agents under deviated cyclic pursuit protocol is considered. The graph is directed in this case. The robustness issue because of the rotation angle in cyclic pursuit protocol is handled by an additional nonlinear function. It is of interest to note that the applied nonlinear function is of Hopf oscillator dynamics which also satisfies the one-sided and quadratic-inner bounded conditions. Poincar'{e} map is used to show the existence of quasi-periodic trajectories. All the designs are validated through numerical simulations.

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