On Consensus And Dissipativity Of Complex Dynamic Systems

In the past decades, distributed computing of networks mainly depends on some workstation consisting of both complex and expensive, but strong functional processors to carry out tasks. With the improvement of computer technology, complex dynamic systems rapidly develop in recent years. Superior performances of multi-agent networks based on complex dynamic systems as well as their more and more possible potential applications have been highlighted day by day. The same purpose can be obtained by using coordination between these simple and low-price agents, which not only save the cost, but enhance overall system's robustness and flexibility. Moreover, agents will be loss of energy during the process.Therefore, research on consensus and dissipativity of complex dynamic systems has aroused many experts' strong interest.The unprecedented upsurge has been raised to study complex dynamic systems in the world.The dissertation has been focused on consensus problems in. singular systems, impulsive systems, as well as random network environment, by applying control theory, algebra graph theory as well as matrix theory, regarding some questions on network communication factors, such as time delay, noise, external disturbance under multi-agent networks as real backgrounds.Since agents in networks not only accept information flow from their neighbor agents, but also suffer from the environment constrains, therefore the multi-agent networks may generally be described as singular systems.This dissertation has studied the multi-agent consensus problems based on singular systems for multi-agent networks, conditions for multi-agent systems to obtain consensus when singular systems are in present and absent of time delay, and then, maximum time delay the multi-agent networks can tolerate, as well as the worst speed convergent to consensus has been studied under the condition that multi-agent network can reach consensus.Robust consensus control problems have been studied when exterior disturbances and model uncertainty exist in the communication network under fixed and switched topologies.The results in this dissertation indicate that constraints from environments have influence on consensus behavior and performance of multi-agent networks.Maximum time-delay that multi-agent networks can tolerate as well as consensus convergence speed is related not only with Laplacian eigenvalues of multi-agent's network topology but also with constraints from network environments.Recently, consensus algorithms are mainly based on continuous-time models and discrete-time models, but these models cannot contain some useful networks in the reality. In real dynamic networks, they are possibly some more complex systems, for example, switching systems or general hybrid systems. In real network, agents are subject to instantaneous disturbance frequently and change suddenly in certain time instant, i.e. they experience impulsive effect. Those phenomena widely exist in biological networks, flying objects and so on. Moreover, agents can obtain information from instantaneous contact with their neighbors. To make the best use of the information, impulsive consensus algorithms have been proposed for multi-agent networks in this dissertation. Consensus conditions, consensus convergence rate, as well as anti-disturbance ability have been studied under fixed and switched topologies for multi-agent networks. For multi-agent networks with time-delay, corresponding problems have been considered. The results in this dissertation indicate that consensus algorithms containing impulsive information have faster consensus convergence speed and bigger maximum time-delay that the multi-agent networks can tolerate than that in usual consensus algorithms of multi-agent network based on continuous-time or discrete-time models.In multi-agent networks, noise is inevitable in information channels. Therefore, agents sometimes accept the information "polluted" by noise. Many experts are interested in consensus problems with communication noise. Since multi-agent networks frequently suffer from external disturbance, it is possible that link relations between agents are reconstructed or fail. Therefore, consensus problems of multi-agent networks with random topology have also been studied by many scholars. Two kinds of influence factors: "polluted" information and random topologies, are simultaneously in real multi-agent networks, therefore, consensus problems have been studied under random topology with communication noise in this dissertation. Conditions on mean square consensus and almost sure consensus have been obtained for multi-agent networks.The results indicate that multi-agent networks can still obtain consensus by applying consensus algorithms with suitable decreasing gain-factors, even if the multi-agent networks have negative connection weights.In real world, systems consisting of groups of organisms are dissipative systems. Dissipativity of complex systems is a new problem for multi-agent networks. Dissipativity, exponential dissipation and stabilization are studied. Some conditions on dissipativity and exponential dissipativity are achieved. Passive and non-expansion properties are also discussed, and switching controllers are designed for the time- delay stochastic systems. Exponential stabilization conditions are derived by using the Lyapunov method in this dissertation.Finally, a summary has been carried out in the dissertation and the further study has been presented.