Research On Sampled-data Consensus Problems Of Multi-agent Systems With Time Delay

In recent years, distributed coordinated control of multi-agent systems has attracted agreat deal of attention of researchers from many disciplines, mainly because not only can itreveal the emergence of natural complex systems, but also it has an extremely wide range ofapplications. Consensus plays a fundmental role in the distributed coordinated control ofmulti-agent systems and has become a hot topic in the control theory field. Becausemulti-agent systems are often in uncertain network environments, information exchangeamong agents contains communication delays due to information transmission and reception.Considering the fact that communication delays may destroy the achievement of consensus,we must investigate the effects of communication delays on the achievement of consensus.Meanwhile, in real applications, although the agent’s dynamic process is continuous, only thedata at the sampling instants can be obtained for the synthesis of control laws. Therefore, it isvery necessary to research the sampled-data consensus problems of multi-agent systems withcommunication delays.In this dissertation we investigate consensus problems of multi-agent systems undercommunication delays and sampled-data, obtaining the following results:(1) We investigate sampled-data consensus of first-order delayed multi-agent systemswith delayed-state-derivative feedback. Different from the previous work, we use thenumerical differentiation for approximately computing the delay derivative, partly solving theproblem that it is difficult for an agent in first-order delayed multi-agent systems applying theconsensus protocol with delayed-state-derivative feedback to obtain its neighbor’sdelayed-state-derivative-feedback information. The discrete-time consensus protocol based onsampled data is proposed, and necessary and sufficient conditions are obtained forguaranteeing first-order delayed multi-agent systems using the consensus protocol withdelayed-state-derivative feedback to asympototically achieve the average consensus.(2) We consider sampled-data consensus of second-order delayed multi-agent systemswith delayed-state-derivative feedback. Different from the previous work, we use thenumerical differentiation for approximately computing the delay derivative, partly solving theproblem that it is hard for an agent in second-order delayed multi-agent systems applying theconsensus protocol with delayed-state-derivative feedback to obtain its neighbor’sdelayed-state-derivative-feedback information. The discrete-time consensus protocol based onsampled data is proposed, and necessary and sufficient conditions are derived forguaranteeing second-order delayed multi-agent systems using the consensus protocol withdelayed-state-derivative feedback to asympototically achieve the stationary consensus.(3) We study consensus of heterogeneous multi-agent systems based on sampled-datawith small sampling delay. The consensus protocol based on sampled-data with smallsampling delay is proposed. The algebra graph theory, the matrix theory, the stability theoryof linear systems and some other techniques are employed to derive the necessary andsufficient conditions guaranteeing heterogeneous multi-agent systems applying the consensusprotocol based on sampled-data with small sampling delay to asymptotically achieve the stationary consensus.