Consensus For Linear Multi-Agent Systems With Packet Dropouts And Its Applications

With the extraordinary progress of computing capabilities,storage space,sens-ing performances,and wireless communication technologies,the coordination of multi-agent systems(MASs)is developed rapidly over the last decade.Coordination means that a group of interconnected identical or non-identical agents is designed to complete a common task cooperatively.Besides,consensus is one of the most fundamental topics of the coordination problem.Since MASs have the advantages of parallelism,equality,and easy upgrading,a great number of researchers have been attracted to the coordina-tion of MASs resulting from its plenty of potential engineering applications.For exam-ple,smart agriculture,smart manufacturing,environment exploration,etc.Hence,it is meaningful and attractive to study the consensus of multi-agent systems.In practical circumstances,the packet dropouts in a wireless communication net-work are usually caused by communication noises,limited bandwidth,or congestion.Moreover,the packet dropouts rate is usually increasing with the increasing number of agents.Packet dropouts can reduce the performance of MASs,and even break the consensus-ability.And the controller design for packet dropouts has not been settled entirely.Hence,studying the consensus for MASs with packet dropouts is necessary.We investigate the consensus problem for networked linear multi-agent systems with Markovian packet dropouts and its applications,which concludes the consensus-ability for linear multi-agent systems and consensus-based collective circular motion control for multi-robot systems.The following works are made.·For discrete linear multi-agent systems(MASs)with Markovian packet dropouts,we investigate the consensus problem.Both identical and nonidentical packet dropouts are studied.For the discrete time MASs under identical packet dropouts,we present the expectation of the total sojourn time of packet dropouts and suc-cessful message transmission.Based on these expectations,a linear consensus controller is designed through analyzing the transient properties of the Markov process such that the MASs can reach consensus almost surely for any initial dis-tribution of packet dropouts.When it comes to the nonidentical packet dropouts where all the packets are independent and stochastic,a Markovian-lossy-channel-based switching model(MLCBS model)is proposed.Based on the MLCBS model,we also propose an easy-to-implement linear consensus controller such that the MASs with nonidentical packet dropouts can achieve consensus almost surely.·For linear multi-agent systems with stochastic packet dropouts,a predictive con-troller is designed to drive the system states to reach consensus.A predictive control framework for MASs is proposed to compensate for packet dropouts,and the details of the predictive controller design for MASs are shown.The decou-pled method is applied to transform the consensus for MASs into stability for the corresponding system,and the cost function measuring consensus for MASs is given.By analyzing the evolution of the cost function,the relationships among the predictive horizon,packet dropouts rate,dynamics of agents,and consensus-ability are found,and a sufficient condition is obtained to make the multi-agent systems achieve mean-square consensus.·For linear multi-agent systems without precise packet dropouts model,the suf-ficient condition of consensus-ability for MASs is studied.Since the strategy of malicious attackers is difficult to be known as a prior,the packet dropouts pat-terns and packet dropouts rate are not available.Our method concentrates on the average time of packet dropouts or message received being active in the long run.Besides,the bound of packet dropouts are used in the presence of attackers.First,we transform multi-agent systems into a multi-mode switching system by the decomposition method and changing steps.Then,the evolution of equivalent system states is analyzed.Finally,a sufficient condition of consensus-ability is obtained.·For multiple nonholonomic robots with packet dropouts,the consensus based cir-cular motion for multiple robots is investigated.We aim to achieve a balanced circular motion centered at a location determined by each robot.A back-stepping-based controller is firstly designed to make all the robots rotate around a common center,the position of which is obtained through executing a consensus algorithm by each robot.Then,the maximum and minimum consensus algorithm and a dis-tributed modified ordinal ranking algorithm are applied to set the rotation radius,angular velocity,and orientation parameters in a distributed manner such that all the robots can uniformly space on the common circle.