Cooperative Control of Multiple Rigid Body Systems

The past decade has witnessed significant advancement of the research on the various cooperative control problems of multiple rigid body systems as more and more complex space missions are performed by multiple spacecraft systems that entail cooperation among different subsystems. In this thesis, we study two cooperative control problems of a group of rigid body systems, which consist of one leader system and a number of follower systems. The first problem is the leader-following consensus problem, which aims to design a distributed control law to drive the attitudes and angular velocities of all followers to a class of prescribed trajectories generated by the leader system. The second problem is the time-varying formation control problem, which involves the design of a distributed control law that makes all the agents achieve a class of time-varying formation configurations on the basis of achieving the same objective as the leader-following consensus problem.In practice, due to the mission requirement and the harsh space environment, the communication between different agents cannot be guaranteed all the time. Thus, it is desirable to design a control scheme that can handle weak communications. Such a control scheme that satisfies some specified communication constraint is called a distributed control scheme. There are various assumptions on communication networks, which can be either static or switching, and can be either connected or disconnected at every time instant. The mildest assumption on the switching communication networks is the so-called jointly connected condition, which is also the most challenging one as this type of communication networks can be disconnected at every time instant. In this thesis, we place our emphasis on solving our two problems over jointly connected communication networks via a so-called distributed observer-based approach. It turns out that this approach is quite effective in overcoming the challenge posed by switching communication networks. This approach consists of three steps. First, solving the problem for the special case where every follower knows the leader's information. The problem for this case is reduced to the tracking problem of some desired trajectory for a single system, and the designed control law is called the purely decentralized control law. Second, design a dynamic compensator called the distributed observer to pass the leader's information to every follower over the switching communication constraint. Third, replace the leader's information in the purely decentralized control law with its estimation from the distributed observer to synthesize a distributed control law. If the distributed control law achieves the same control objective as the purely decentralized control law, then we say this distributed control law satisfies the certainty equivalence principle. It is noted that, unlike the linear time-invariant systems which always satisfy the certainty equivalence principle, the dynamics of rigid body systems are highly nonlinear, and the closed-loop system may exhibit finite escape time, thus, the certainty equivalence principle may not hold. Therefore, we have to perform rigorous stability analysis to ascertain the satisfaction of the certainty equivalence principle case by case.We divide this thesis into two parts. In the first part, we study the leader-following consensus of multiple rigid body systems over jointly connected networks under various scenarios described as follows:1. The leader-following consensus problem of multiple rigid body systems by attitude feedback is studied. On one hand, to handle the discontinuity of the closed-loop states caused by the switching communication network, we employ the generalized Barbalat's Lemma to carry out a stability analysis. On the other hand, we relax the restrictive requirement on the initial condition of the auxiliary system in the literature such that our result is almost global.2. The leader-following adaptive consensus with unknown disturbance rejection problem of multiple uncertain rigid body systems is studied. First, we solve a special case of this problem where there is no external disturbance with an adaptive control technique. Then, we introduce unknown bounded external disturbance to the plant dynamics and further study this general case. Moreover, the methodology of handling the unknown external disturbance can be applied to the leader-following consensus and disturbance rejection problem of multiple uncertain Euler-Lagrange systems. The corresponding result is also included in this part as an application.3. The leader-following event-triggered adaptive practical consensus problem of multiple uncertain rigid body systems is studied. We modify the conventional parameter update law to a novel one that leads to a desirable Lyapunov-like analysis. Moreover, due to the existence of the event-triggered mechanism, we further show that the closed-loop system prevents the Zeno phenomenon from happening.In the second part, we study the time-varying formation control problem over both static and jointly connected switching communication networks.1. The case where the communication network is static is first considered. First, we use an exosystem, which can produce a large class of time-varying signals, to generate the leader's trajectory as well as the formation configuration, so that we can achieve a variety of time-varying formations. Second, we extend the distributed observer to the form that estimate not only the leader's attitude information, but also the leader's position and the desired relative positions between the leader and all the followers. What is more, unlike the consensus problems in the first part, where the distributed control laws are synthesized by replacing the leader's information in the purely decentralized control laws with its estimation, we further add a compensation term to furnish a successful stability analysis.2. The case where the communication network is jointly connected is then studied. We first extend the distributed observer for the leader's position such that it can handle jointly connected communication networks. Then, the stability analysis is performed by invoking the generalized Barbalat's lemma.1.研究靜態通信網絡的情形。首先，我們採用一個能夠產生一大類時變信號的外部系統來生成領導者的軌跡和編隊構型，從而可以實現多種時變的編隊。其次，我們將分佈式觀測器推廣至不僅能夠估計領導者的姿態，而且能夠估計領導者的位置，以及領導者與跟隨者間期望的相對位置的形式。此外，與在第一部分考慮的領導者-跟隨者一致性問題中，分佈式控制律是將純粹的分散式控制律中領導者的信息由它的估計值替換而得到不同的是，我們額外加了一個補償項以實現成功的穩定性分析。2.進一步研究聯合聯通的通信網絡的情形。我們首先推廣了對領導者姿態的分佈式觀測器，使其能夠處理聯合聯通的通信網絡的情形。隨後通過調用廣義Barbalat引理來進行穩定性分析。近十年來，由於越來越多複雜的太空任務需由多個航天器系統共同執行，從而引發了多個航天器系統的協同控制問題。目前多剛體系統的各種協同控制問題的研究正在取得重大進展。本文研究了由一個領導者與若干跟隨者組成的一組剛體系統的兩個協同控制問題。第一個問題是領導者-跟隨者一致性問題，其旨在設計一個分佈式控制律來使所有跟隨者的姿態及角速度達到一類由領導者系統生成的規定軌跡。第二個問題是時變的編隊控制問題，此問題為設計一個分佈式控制律，使得所有的系統在實現與領導者-跟隨者一致性問題相同的控制目標的基礎上，達到一類時變的編隊構型。在實際應用中，由於任務要求及複雜的空間環境，不同系統間的連通性不能被時刻保證。因此，我們希望設計出一個能夠承受弱通信的控制律。此種滿足某個特定的通信約束的控制律稱作分佈式控制律。關於通信網絡有種類繁多的假設。通信網絡既可以是靜態的也可以是切換的，可以是時刻聯通的也可以是時刻不聯通的。其中所謂的聯合聯通條件允許該通信網絡時刻不聯通，因此是關於切換通信網絡最寬鬆的假設，因而也是最有挑戰性的條件。本文著重於通過基於所謂分佈式觀測器的方法，在聯合聯通的通信網絡下解決我們的兩個控制問題。研究結果表明，此方法可以十分有效地克服由切換通信網絡帶來的挑戰。該方法包含三個步驟。第一步為在每個跟隨者都知道領導者信息的特殊情況下求解該問題。此種情況下，問題被簡化成為單系統對某個期望軌蹟的追蹤問題，所設計出的控制律稱為純分散式控制律。第二步，設計一個稱作分佈式觀測器的動態補償器，以在切換的通信約束的條件下將領導者的信息傳遞給每一個跟隨者。第三步，通過將純粹的分散式控制律中領導者的信息由分佈式觀測器提供的估計值替換，以合成一個分佈式控制律。如果分佈式控制律能夠實現與純分散式控制律相同的控制目標，則我們稱此分佈式控制律滿足確定性等價原理。需要注意的是，與確定性等價原理恆成立的線性時不變系統不同，剛體系統的動力學模型是高度非線性的，其閉環系統可能出現有限逃逸時間，因而確定性等價原理不一定成立。因此，我們必須針對每一具體問題進行穩定性分析，以驗證確定性等價原理是否滿足。本文分為兩部份。第一部份研究了聯合聯通網絡下的多個剛體系統在如下各種情形下的領導者-跟隨者一致性問題，簡介如下：1.研究通過姿態反饋的多剛體系統領導者-跟隨者一致性問題。一方面，我們在穩定性分析中採用廣義Barbalat引理來處理由切換通信網絡引起的閉環系統狀態不連續的問題。另一方面，我們改進了參考文獻中對輔助系統初始值的限制性約束條件，從而獲得幾乎全局的結果。2.研究多個不確定剛體系統的領導者-跟隨者自適應一致性與未知擾動抑制問題。首先，我們通過自適應控制方法解決了系統沒有外部擾動的特殊情況。隨後，我們在系統的動力學模型中加入了未知的有界外部擾動，並進一步研究了該一般情況。值得一提的是，我們處理未知外部擾動的方法也可以被應用在多個不確定Euler-Lagrange系統的領導者-跟隨者一致性及擾動抑制問題。相應的結果作為應用同樣包含於此部分中。3.研究基於事件觸發的多剛體系統領導者-跟隨者實際一致性問題。我們將既有的參數更新律修改為一種新的形式以實現期望的Lyapunov分析。此外，由於事件觸發機制的存在，我們進一步證明了閉環系統不會出現芝諾現象。本文第二部份研究了在靜態通信網絡與聯合聯通的切換通信網絡下時變的編隊控制問題。WANG, Tianqi.Ph.D. Chinese University of Hong Kong 2021.Includes bibliographical references (leaves )Abstracts in English and Chinese.Title from PDF title page (viewed on ...