摘要
随着计算机、通信，以及传感等技术的不断发展，多自主体系统在诸如军事、工业生产、航空航天、经济等领域获得了广泛的应用，因此，在近些年来越来越多的学者投身于多自主体系统的研究。一致性问题是多自主体系统协作控制中最为基础的研究方向之一。考虑到许多实际系统中对一致性快速实现的需求，尤其是对于有高精度和高速度以及控制能耗要求的控制问题，本文在分析了现有研究成果的不足的基础上，针对几个不同的方面，提出了几种不同的有限时间一致性协议，使得多自主体系统的一致性能够在有限时间内实现。
首先，针对连续的一致性控制带来的控制能耗大的问题，分别研究了无领航者和领航者-跟随者多自主体系统的有限时间一致性问题，提出了两种非线性的事件触发控制策略，明显地减少了控制器更新频率和控制能量消耗，同时，还加快了系统的一致性收敛速度，提高了系统抗干扰能力，延长了系统寿命。此外，还给出了触发间隔时间的下界，保证了Zeno行为不存在。
其次，针对科技和工程应用领域中，许多系统都会在运动过程中的某些固定时刻或者非固定时刻会出现状态瞬间突变的现象，基于脉冲控制理论，提出了两种脉冲有限时间一致性控制协议，分别研究了无领航者和领航者-跟随者两种情况下的多自主体系统的脉冲有限时间控制问题。给出了充分条件来保证所提出的控制协议比无脉冲情形下的有限时间控制协议具有更快的收敛速度，进一步满足实际控制系统对高速度的需求。同时，还可以通过间歇地(而非连续地)发送领航者状态信息到(至少)一个跟随者自主体，来实现系统运动过程对系统一致状态的改变，满足实际控制系统对高精度的需求。
然后，针对自主体之间通信链路能够保持的情形，研究了固定拓扑结构下的一阶和二阶多自主体系统的有限时间一致性问题，分别设计了非线性的控制协议，给出了多自主体系统有限时间一致的充分条件。接下来，针对环境中障碍物的出现或者通信网络故障等因素造成的自主体之间通信链路的增加或者缺失，使得自主体之间的拓扑结构出现切换或者不连通的情况，又分别研究了固定拓扑和两种切换拓扑下的领航者-跟随者多自主体系统的有限时间一致性问题，引入了分布式的误差函数，以及并图的概念，进而设计了分布式的非线性控制协议，分别提出了基于固定拓扑、切换拓扑，以及切换并图的连通性的多自主体系统有限时间一致的充分条件。
最后，针对实际应用中，复杂环境的影响以及任务分工的不同，组成多自主体系统的个体可能具有不同功能或者动力学特性的情况，研究了由一阶和二阶自主体组成的异构多自主体系统的有限时间一致性问题，设计了异构的非线性控制协议，根据Lyapunov理论，得到了在无论领航者为一阶或者二阶自主体，还是静态或者动态自主体的情形下，异构多自主体系统的一致性都能够在有限时间内实现的充分性条件。
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.
引文
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