| With the development of technologies of computer, communication, and sensor,multi-agent systems have wildly applied in many fields, such as military affairs, industries,aerospace, economic, and so on. So, more and more researchers devote themselves to thestudy of multi-agent systems. Consensus is one of the most basic aspects in thecoordination control of multi-agent systems. Considering the requirement of fastconsensus speed in many practical systems, especially some control problems with highprecision and high speed requirement, some different finite-time consensus protocols areproposed from some different aspects, based on the analyzing of the lack of existingresults, such that the consensus of multi-agent systems can be achieved in finite time.Firstly, in order to overcome the problem of huge consumption of energy brought bycontinuously communication among agents, two nonlinear event-triggered controlstrategies are proposed for leadless and leader-follower multi-agent systems, respectively.Finite-time consensus can be achieved and the convergence speed can be speeded upunder proposed protocols, meanwhile, the consumption of energy and the frequencies ofcontrollers updating can be reduced, the capacity of resisting disturbance is improved, andthe system life is prolonged. Moreover, the bound of the triggering interval is provided toillustrate that no Zeno behavior exists.Secondly, consider that in the fields of technique and engineering applications, manysystems may encounter the phenomena of state changed instantaneously at some regulartimes or irregular times, two impulsive finite-time consensus protocols are proposed basedon the impulsive control theory. The impulsive finite-time consensus problems are studiedfor leadless multi-agent systems and leader-follower multi-agent systems, respectively.Sufficient conditions are given to ensure that the proposed control protocols have a muchfaster convergence speed than the finite-time protocols without impulse, which satisfy thehigh speed requirements of some practical control systems. Meanwhile, according tointermittently (rather than continuously) send the leader’s state to at least one follower, thechange of consensus state can be realized in the process of systems achieving consensus, which satisfy the high precision requirements of some practical control systems.Thirdly, consider the situation that the communication links of multi-agent systemscan be maintained, the finite-time consensus problems of first-order and second-ordermulti-agent systems with fixed communication topology are studied, nonlinear controlprotocols are respectively designed, and some sufficient conditions are given formulti-agent systems to achieve finite-time consensus. Then, consider the complicatedenvironment, in which the system topology can be switching or even unconnected due tothe appearing of obstacles or the adding or losing of links cased by the failed ofcommunication, the finite-time consensus problems of leader-follower multi-agentsystems with fixed topology and two kinds of switching topology are studied, respectively.Distributed error functions and the concept of union graphs are introduced, and distributednonlinear control protocols are designed accordingly. Sufficient conditions are proposedfor multi-agent systems with fixed topology, switching topology, and switching uniontopology, respectively.Finally, contrapose the situation that the agents in a multi-agent system may havedifferent functions or dynamics in practical applications due to the affection ofcomplicated environment and the different division of work, the finite-time consensusproblems of heterogeneous multi-agent systems composed of first-order and second-orderagents are studied. Nonlinear heterogeneous control protocol is designed. Based on theLyapunov theory, some sufficient conditions are obtained for heterogeneous multi-agentsystems to achieve (static or dynamic) consensus in finite time, no matter the leader is afirst-order or a second-order agent. |
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