Synchronization And Consensus Of Complex Multi-agent Networks With Time Delays

In practice, complex multi-agent networks are widely used, such as wireless sensor networks, unmanned aerial vehicles, multi-robot systems and automatic highway systems, etc. The main purpose of the research on complex multi-agent networks is to accomplish complex tasks by the coordination and cooperation among a large scale of agents instead of an expensive single system. In the process of cooperation and coordination, each agent shares information through network, where the information including control algorithm, common target or relative position information. In order to achieve effectively cooperative control, agents need to reach agreement on the task. Thus, the study on synchronization and consensus, as the foundations of cooperation and coordination between agents, becomes an important research topic in the field of system and control. However, due to the introduction of network, the information exchanges among agents will be influenced inevitably by time delays, which would deteriorate the performance of the whole network. Therefore, based on previous investigations of the others, this dissertation further studies the synchronization and consensus of complex multi-agent networks with time delays by combining the stability theory, algebraic graph theory and stochastic analysis method together. The main research contents and achievements of this dissertation include the following aspects:Synchronization of complex dynamical networks with stochastic communication delay. Considering that the communication delay contains different delay forms for the first time, and the occurrence probability of each delay form is assumed to be known in prior. In order to facilitate the analysis, some indicator functions are introduced to transform the original system with stochastic delay into another multiple delay system with indicator function based stochastic system parameters. By utilizing a novel Lyapunov-Krasovskii stability theory and stochastic analysis techniques, a sufficient criterion for the asymptotical synchronization in the mean square is obtained, and the maximum delay that the network can tolerate depends on both the bounds and the occurrence probabilistic of each delay form.Synchronization of complex dynamical networks with additive stochastic communication delays. Note that the communication delay considered in most of the existence works is actually a rough summary of several different kinds of delays caused by diverse facts, which ignore the fact that additive delays in actual systems may contain different statistical properties and it is not rational to lump all of them into one. Considering these facts, additive stochastic delays in complex dynamical networks are taken into consideration, where the nodes-induced delay is subject to an i.i.d stochastic process and the network-induced delay is governed by a Markov chain. By utilizing a novel Lyapunov-Krasovskii functional and stochastic analysis techniques, a sufficient criterion is obtained to ensure the synchronization of the network, which reveals that the upper bound of the sum of additive delays and the upper bound of the sum of delay derivations, as well as the statistical characteristics of delays, have effect on the synchronization performances of the CDN.Exponential synchronization of Markovian jump complex dynamical networks with mixed delays. As network topology switching is a universal phenomenon in actual systems, the exponential synchronization problem for complex dynamical networks with Markovian jump parameters and mixed delays is investigated. Both the discrete and distributed delays are taken into consideration, where the distributed delay is bounded and time-varying and the discrete time delay is stochastic and time-varying. Some indicator functions are introduced to transform the original network with stochastic delays into another multiple delayed network with indicator function based stochastic system parameters. By utilizing the Lyapunov-Krasovskii stability theory and stochastic analysis techniques, some sufficient exponential synchronization criteria are obtained, and the maximum values of delays that the network can tolerate depend not only on the size of the mixed delays, but also on the occurrence probability distribution of the stochastic discrete time delay. Moreover, the main criterion derived in this work can be successfully extended to multi-agent systems with Markovian jump parameters and stochastic communication delay, and a sufficient condition is derived to ensure the system achieve consensus.Consensus in Markovian jump second-order multi-agent systems with random communication delay. Considering a more practice network communication mode, such as peer-to-peer(P2P) network, both the coupling weights and state information need to be transmitted through network, which will be suffered by the communication delay. For such a class of second-order multi-agent systems with time delay and switching topology, where the stochastic switching signal and the random communication delay are dominated by two mutually independent Markov chains, a novel consensus protocol is presented without using the neighbors' velocity information. By preforming three steps of model transformation and introducing a new mapping for the two independent Markov chains, the original system is converted into an expanded analogous error system with two Markovian jumping parameters. A necessary and sufficient criterion for the mean square consensus of the system is derived finally.Consensus in second-order multi-agent systems via impulsive control with heterogeneous delays. For a class of second-order multi-agent systems, an impulsive control protocol using position-only information with heterogeneous communication delays is proposed to study the consensus problem of the system, where only the delayed sampled relative positions to neighbors and the relative position to the last sampling state are utilized. By introducing some virtual subgraphs and performing three steps of model transformation, the consensus problem of original continuous-time system is converted to the stability problem of a discrete-time expanded error system. Some necessary and sufficient criteria are derived to guarantee the dynamic average-consensus of the multi-agent systems. Furthermore, a special case, that is, the heterogeneous delays less than one impulsive period, is discussed for both the undirected and directed graph cases, which reveal the influences of the network topology, the impulsive period and the control gains to the consistency of the multi-agent systems.