Study On Event-triggered Control Protocols For Multi-agent Systems

Multi-agent systems have a broad application prospect and the research results have been widely applied in robotic formation, traffic management, unmanned aerial vehicles, underwater vehicle and so on. In the numerous research topics of multi-agent systems, consensus problem is one of the most research value topics. However, in the traditional control protocols for the consensus of multi-agent systems, achieving consensus needs a great number of data transmissions and requires the system to be equipped with high performance processors. In order to effectively reduce the data transmission and the requirement of processors, event-triggered control protocol is introduced into the consensus of multi-agent systems.In this thesis, we will study the event-triggered control protocols for the consensus of multi-agent systems, and the main works are divided into the following several aspects:① The consensus problem of the multi-agent systems with input delay is studied and the corresponding event-triggered control protocol is proposed. Focusing on the first-order linear multi-agent systems, we assume that the internal coupling matrix of the system is stabilized and the communication topology of the system has a directed spanning tree. Then the sufficient condition is analytically obtained and also presents that the proposed event-trigger control protocol is feasible. Furthermore, the theoretical results show that the system can reach consensus under the proposed event-triggered control protocol only if the input delay does not exceed a certain upper bound. Meanwhile, the expression of the upper bound is provided, which shows that the upper bound is associated with communication topology of the system and is independent of the parameter setting in the event-triggered control protocol.② We find and point out that the proofs of excluding Zeno-behavior in the existing event-triggered control protocol based on continuous sampling are not rigorous. On the one hand, the existing proofs generally assume that the local consensus cannot be reached before the global consensus. Such assumption can assure that the threshold in the event-trigger control protocol is nonzero before the global consensus reached, but it is unreasonable. On the other hand, the existing proofs generally assume that the positive event-trigger intervals can exclude Zeno-behavior. However, we analytically conclude such condition is not enough sufficient to exclude the Zeno-behavior. Therefore, we introduce a time-varying offset into the proposed event-triggered control protocol to ensure that the threshold in control protocol is positive to avoiding the Zeno-behavior induced by the local consensus. In addition, we also take the noise of the practical applications into account, and the introduction of the offset can also avoid the Zeno-behavior arisen from the noise.③ The consensus problem of the random sampling multi-agent systems is studied and the corresponding event-triggered control protocol is proposed. In practical applications, it is hard to be guaranteed that the continuous sampling and the periodic sampling, and therefore it is necessary to study the event-triggered control protocol based on the random sampling. Moreover, the event-trigger control protocol based on the random sampling has the following advantages: 1) Because of the sampling interval, the event-triggered interval is definitely greater than zero and not infinitesimal, which means the Zeno-behavior will not be induced; 2) The event-triggered function in the control protocol is only calculated at each sampling instance, which can greatly save the computational recourses; 3) The number of the data transmission and controller update can be reduced to a certain extent. Meanwhile, focusing on the second-order multi-agent systems and considering that the existing threshold is no longer applicable, we combine the state-dependent threshold and the time-dependent threshold to propose a combined threshold. The combined threshold can overcome the defects that the value of state-dependent threshold is small and the time-dependent threshold cannot be adjusted according to the initial state of the system. Compared with the existing event-triggered control protocol, the event-trigger control protocol based on the combined threshold can get the same control goals by less event triggers, which can greatly reduce the number of information transmissions and controller updates.④ The leader-following consensus problem of the multi-agent systems is studied and the corresponding event-triggered control protocol is proposed. In practical applications, it is possible that the topology of the system cannot satisfy the sufficient condition of consensus, and thus it is necessary to introduce the pinning control into the multi-agent systems. The typical pinning control in multi-agent systems is leader-following consensus control, and thus it is gerat research significant. In the proposed event-triggered control protocol, the leader sends its sampling data to the followers at each sampling instant, and the followers’ event-triggered function has two measurement errors. In such way, it is solved that the follosers cannot send sampling data to the leader and the leader cannot set the corresponding event.⑤ The consensus problem of the multi-agent systems with the quantization mechanism is studied and the corresponding event-triggered control protocol is proposed. In practical applications, the communication channels have the limited capacity of transmitting data and the accuracy of the transmitting data is also limited, and thus it is necessary to introduce the quantization mechanism to the event-triggered control protocol. By introducing the quantization mechanism into event-triggered control protocol, the sampled data can be represented by fewer bits, so the objective of reducing control costs can be achieved. Not only that, for further reducing control costs, we combine the existing relevant mechanisms in the proposed event-triggered control protocol, such as periodic sampling mechanism, self-triggered mechanism and the encode-decode mechanism.