针对已有的一阶有向网络一致性分析结果在高阶网络的应用问题，从图论角度入手，给出了高阶多智能体网络一致性分析的新结果。通过模型变换，在一定条件下，将个体动态为高阶积分器模型的有向网络的系统矩阵变换为具有零行和的Metzler矩阵。由此采用图论、非负矩阵理论和控制理论工具，将一阶有向网络的一致性分析结果拓展到了高阶情况。针对固定拓扑，分别给出无领航和领航—跟随两种情况下的一致性条件及一致状态。并且证明动态拓扑情况下，在有限的拓扑切换时间间隔内，若有向图联合具有生成树，则整个闭环动态网络实现渐近一致。仿真实例和多车辆编队控制仿真验证了分析结果的正确性。
Abstract
New results are put forward for consensus analysis of high-order multi-agent network from the perspective of algebraic theory, subject to the application problem of existing consensus analysis achievements of first-order directed network in high-order network. Under certain condition, the system matrix of directed network is Metzler with zero row sum by model transformation where the dynamics of agents is modeled as a high-order integrator. Thus the analysis results of first-order consensus algorithms are extended to high-order ones using algebraic theory, nonnegative matrix theory and control theory. The consensus conditions and consensus states are proposed for leaderless and leader-follower cases in fixed topology. Moreover, it is proved that the whole closed-loop network achieves consensus asymptotically if the union of directed graphs across finite switching intervals has a spanning tree in dynamic switching topology. Simulation examples and multi-vehicle formation control simulation validate the soundness of the theoretical results.
关键词
自动控制技术 /
一致性 /
高阶多智能体网络 /
动态拓扑 /
多车辆编队控制
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Key words
automatic control technology /
consensus /
high-order multi-agent network /
dynamically switching topology /
multi-vehicle formation control
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参考文献
［1］ VicsekT, Czirok A, Ben-Jacob E, et al. Novel type of phase transition in a system of self-driven particles[J]. Physical Review Letters, 1995, 75(6):1226-1229.
[2] JadbabaieA, Lin J, Morse A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules[J]. IEEE Transactions on Automatic Control, 2003, 48(6): 988-1001.
[3] Olfati-SaberR, Murray R M.Consensus problems in networks of agentswith switching topology and time-delays[J]. IEEE Transactions on Automatic Control, 2004,49(9): 1520-1533.
[4] RenWei, Beard R W, McLain T W.Coordination variables and consensus building in multiple vehicle systems[M]∥Lecture Notes in Control and Information Sciences, New York: Springer-Verlag, 2004: 171-188.
[5] RenWei, Beard R W. Consensus seeking in multi-agent systems under dynamically changing interaction topologies[J]. IEEE Transactions on Automatic Control, 2005,50(5): 655-661.
[6] RenWei, Beard R W. Distributed consensus in multi-vehicle cooperative control: theory and applications[M].London: Springer, 2008: 89-96.
[7] TannerH G, Jadbabaie A, Pappas G J. Flocking in fixed and switching networks[J]. IEEE Transactions on Automatic Control, 2007,52(5): 863-868.
[8] XieGuangming, Wang Long. Consensus control for a class of networks of dynamic agents[J].International Journal of Robust and Nonlinear Control, 2007, 17:941-959.
[9] LinPeng, Jia Yingmin. Consensus of second-order discrete time multi-agent systems with nonuniform time-delays and dynamically changing topologies[J]. Automatica,2009,45:2154-2158.
[10] Olfati-SaberR, Fax J A, Murray R M. Consensus and cooperation in networked multi-agent systems[J]. Proceedings of the IEEE,2007, 95(1): 215-233.
[11] RenWei, Beard R W, Atkins E M. Information consensus in multivehicle cooperative control[J].IEEE Control System Magazine, 2007, 6: 71-82.
[12] RenWei,Moore K,Chen Yangquan. High-order and model reference consensus algorithms in cooperative control of multi-vehicle systems[J]. ASME Journal of Dynamic Systems, Measurement, and Control, 2007, 129(5):678-688.
[13] JiangFangcui,Wang Long,Jia Yingmin.Consensus in leaderless networks of high-order-integrator agents[C]∥Proceedings of American Control Conference, St. Louis,2009:4458-4463.
[14] 林鹏.多智能体系统一致性控制及其在编队中的应用[D].北京:北京航空航天大学,2009:65-69.
LIN Peng.Consensus control of multi-agent systems and its applications to formations[D]. Beijing: Beihang University,2009,65-69. (in Chinese)
[15] WolfowitzJ. Products of indecomposable, aperiodic, stochastic matrices[C]∥Proceedings of the American Mathematical Society, 1963:733-736.
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脚注
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