Research On Consensus Tracking Problems Of Multi-Agent Systems Based On Sampled-Data Control

In the past several years, many researchers at home and abroad have presented various consensus protocols of multi-agent systems and studied the convergence by effective mathematical tools and stability analysis methods, which promote the development of the research on consensus problems of multi-agent systems. Compared with the continuous-time systems with continuous-time controller or discrete-time systems, the continuous-time systems based on sampled-data control have a certain advantage in control accuracy, control speed and control performance. In addition, different from the high traffic of full-state information transmission, the measurements only at sampling instants can effectively save the network bandwidth and communication cost. Thus, we take the multi-agent systems based on sampled-data control as the research object, and discuss the consensus problems of first-order multi-agent system, second-order multi-agent system and heterogeneous multi-agent systems.Moreover, in real applications, all the agents are often required to converge to a desired common value, which evolves over time. This can be classified as the consensus tracking, where each agent exchanges its own state information with its neighbors or the virtual leader such that all the agents track the virtual leader. While applying the traditional x-consensus protocols, the achieved final consensus states of the multi-agent systems are functions of all the agents’ initial states, which can’t solve the problem of consensus tracking. As a given reference model, the consensus tracking problems have certain universality, so this dissertation is concerned with the consensus tracking problems of the multi-agent systems based on sampled-data control.First the bounded tracking consensus problems of first-order multi-agent systems under undirected network topology and directed network topology are studied, respectively. According to the proposed tracking protocol, the convergence of the system is analyzed. Because of delays might cause the system to oscillate or diverge, thus the delay effects on stability of multi-agent systems cannot be ignored. Two cases of sampling delay less than a sampling period and more than a sampling period in multi-agent systems have been considered. When the sampling delay is less than a sampling period, the necessary and sufficient conditions guaranteeing the bounded consensus tracking are relatively simple, which is the supremum and infimum of sampling period and sampling delays. When the sampling delay is greater than the sampling period, however, the obtained theoretical results is more complex. Especially under the directed network topology, due to the asymmetry of the corresponding adjacence matrix, it is difficult to find the explicit expression of sampling period and sampling delays.Secondly, in the practical engineering, there are many multi-agent systems composed of such as unmanned aerial vehicles or robots, whose control input is not the velocity variables, but the second derivative of the position variables, that is the acceleration variables. Therefore, we extend the research results about first-order systems to the second-order multi-agent systems. When each agent can use the position and velocity information measured at the sampling instants from its neighbors or the virtual leader with a time-varying reference state,the consensus problems of the second-order multi-agent systems is discussed with the use of algebraic graph theory, matrix theory, the delay decomposition approach, the augmented matrix method and the frequency domain analysis. In addition, considering that the velocity information is more difficult to obtain than the position information owing to technology limitation or environmental disturbances, hence the consensus tracking protocols such that all agents can still reach consensus on their states in the case that the velocity information is not measure directly are designed in this dissertation. Then the necessary and sufficient conditions of bounded consensus tracking under undirected network topology and the sufficient conditions of asymptotically consensus under directed network topology are obtained, respectively, which show that the convergence of systems is related to network topology structures, control parameters, sampling periods, sampling delays and other factors.The above research on the consensus problems of first-order and second-order multi-agent systems, is all assuming each agent with the same-order integrators. In a large-scale system, however, because of various environmental restrictions or uncertainty, it’s hard to ensure all the agents have the same dynamic characteristics sometimes. In this study, the consensus tracking problems of heterogeneous multi-agent systems are considered, which is composed of first-order and second-order integrator agents for the common tracking goals.The corresponding consensus tracking protocols are proposed, and employing algebraic graph theory, matrix theory and Lyapunov stability analysis method, the validity of consensus tracking protocols of heterogeneous multi-agent systems is proved based on the characteristics of the topology of the network connectivity.Finally,all discussions in the dissertation is summarized, and several issues worthy of further work are presented.