Abstract
Cooperative control of multi-agent systems has drawn much interest in the past decades because of its broad application in many areas such as sensor networks, networked mobile robots, unmanned aerial vehicles and so on. Various cooperative control problems including, but not limited to, consensus, containment, and formation, have been widely investigated. The distributed controllers are usually employed to deal with these cooperative control problems, where each agent has only access to the information of itself and its neighboring agents. In many practical systems, communication topologies among agents usually suffer from abrupt variations in their structures because of random link failures and sudden disturbances. The Markovian switching topologies are commonly used to model these changing graphs, and thus have attracting considerable attention from the control community in the past years. On the other hand, time-delays are often inevitable in practice and often lead to poor performance or even instability of various systems including multi-agent systems. Most existing works on cooperative control problems of multi-agent systems take either Markovian switching topologies or time-delays into consideration. However, in real-world applications, Markovian switching topologies and time-delays often occur simultaneously, and they should be handled at the same time.Motivated by these observations, this thesis investigates several cooperative control problems of heterogeneous multi-agent systems with Markovian switching topologies and time-delays. This thesis can be divided into two parts. The first part studies the leader-following consensus and the containment problems of heterogeneous linear multi-agent systems with bounded communication delays via the distributed observer approach. The main results of this part can be summarized as follows.
1. The leader-following consensus problem of heterogeneous multi-agent systems with Markovian switching topologies and time-varying delays is studied. By modeling the switching topologies as a time-homogeneous Markov process and taking the communication delays into consideration, a distributed observer is proposed to estimate the state of the leader. A novel distributed output feedback controller is then designed. It is shown that the closed-loop system can reach mean square leader-following output consensus under an easily-verifiable sufficient condition.
2. The containment control problem of heterogeneous multi-agent systems with Markovian switching topologies and distributed delays is investigated. A novel distributed containment observer is proposed to estimate the convex hull spanned by the leaders' states. A novel distributed output feedback containment controller is then designed without using the prior knowledge of distributed delays. By constructing a novel switching Lyapunov functional, it is shown that the output containment control problem is solved in the sense of mean square under an easily-verifiable sufficient condition.
The second part of this thesis considers the leader-following consensus and the formation-containment control problems of heterogeneous linear multi-agent systems with unbounded distributed communication delays via the distributed observer approach, where the prior knowledge of the unbounded delays is not required to be known. The main results of this part are summarized as follows.
1. The leader-following consensus problem of heterogeneous multi-agent systems with Markovian switching topologies and unbounded communication delays is considered. The main challenge of the concerned problem arises from how to address unbounded communication delays and Markovian switching topologies simultaneously. A novel distributed observer is developed based on a newly proposed Lyapunov functional method. Then, a distributed controller based on the observer is designed. It is shown that the distributed leader-following consensus problem is solved in the sense of mean square if the union graph of the underlying Markovian switching topology contains a spanning tree. A distinctive feature of the proposed controller is that no prior knowledge of unbounded communication delays is required.
2. The formation-containment control problem of heterogeneous multi-agent systems with Markovian switching topologies and unbounded communication delays is considered. The multi-agent system consists of a reference leader with a desired trajectory, a group of formation-leaders with a prescribed formation, and a group of followers. Novel distributed controllers are proposed for the formation-leaders and followers, respectively, without prior knowledge of the unbounded communication delays. It is shown that under the proposed distributed controllers, the outputs of the formation-leaders not only achieve the predefined time-varying formation but also track the desired trajectory generated by the reference leader in the sense of mean square, while the output of each follower converges to the convex hull spanned by the outputs of those formation-leaders in the sense of mean square.
| Date of Award | 17 Aug 2023 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Gang Gary FENG (Supervisor) & Siyang GAO (Co-supervisor) |