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基于模型参考的异构多智能体平均一致性

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  摘 要:针对参数未知的异构线性多智能体系统,在无向或平衡有向网络下提出一种固定输出平均一致性协议,使得每个智能体的输出达到它们初始输出的平均值。首先,网络中每个智能体都被建模成阶数不同且相关度为1或2的未知线性系统,并根据自身及其邻居节点的输出更新其状态;其次,基于模型参考控制方法,对不同相关度的智能体定义相对应的模型;最后,提出一致性协议使每个智能体的输出收敛至其参考模型的输出,即达到固定输出平均一致。仿真实验利用了一个说明性的例子验证了所提协议的有效性和收敛性。
  关键词: 多智能体系统;异构;参数未知;平均一致性;模型参考
  中图分类号:TP273
  文献标志码:A
  文章编号:1001-9081(2019)04-1240-07
  Abstract: Focusing on heterogeneous linear Multi-Agent System (MAS) with unknown parameters, a fixed output average consensus protocol was proposed in undirected or balanced directed network to make the output of each agent reach the average of their initial output. Firstly, each agent in the network was modeled as an unknown linear system with different order and correlation of 1 or 2, which state was updated according to the output of its own and neighboring nodes. Then, based on the model reference control method, the corresponding models were defined for the agents with different correlations. Finally, a consesus protocol was proposed to converge the output of each agent to the output of its reference model, achieving the average consesus of fixed output. The simulation with an illustrative example demonstrates the effectiveness and convergence of the proposed protocol.
  Key words: Multi-Agent System (MAS); heterogeneity; parameter unknown; average consensus; model reference
  0 引言
  近年來,鉴于在人工智能、编队控制与网络控制等众多领域的应用中有着灵活且廉价的优点[1],多智能体系统的控制逐渐成为一个热门的研究领域[2-3],其中一个重要的问题是多智能体系统的一致性问题。在没有全局控制与整体通信的情况下,每个智能体如何仅凭自身及其邻居节点的信息更新其自身状态成为了问题的关键。
  目前为止,关于同构多智能体的一致性研究较多:文献[4]考虑了非最小相位非线性多智能体系统的输出一致性问题,为使系统在存在不稳定零动态动力学的情况下达成一致,提出了一种由两项组成的一致性协议;文献[5-6]从切换拓补、一阶/二阶模型、周期采样策略等角度利用代数图论、Lyapunov理论和矩阵理论分析了多智能体系统的一致性问题;文献[7]进行了高阶多智能体系统的平均一致性研究,在有向网络下,提出的协议使所有速度、加速度与其他高阶状态收敛至0。
  然而,在实际情况中,系统的状态空间结构不尽相同,因此,对于异构多智能体的研究显得十分重要,目前国内外研究人员已经取得了一定的成果:文献[8]在无向网络下,给出了一阶部分输入有界与二阶速度不可测的异构多智能体系统的控制设计方法,基于图论知识与LaSalle不变集,得出了系统一致的充分条件;文献[9]针对异构多智能体系统,提出了一种功率积分器方法并给出了两种一致性协议,其中对于无领导者与有领导者的系统给出了一种连续时间一致性协议,对于设计有限时间观测器,则给出了一种输出反馈有限时间一致性协议;文献[10]将文献[7]中的结构改为异构情况,考虑了固定输出平均一致性在飞行器的应用。然而,文献[8-10]在考虑智能体系统时,没有考虑参数未知的情况。文献[11]利用邻居智能体的输出,研究了相关度为1的均匀未知线性智能体系统,当连通图为强连通图时,提出的协议可使系统达成一致,并同时得出了模型在子系统渐进输出的情况下实现输出跟踪的方法。文献[12-13]利用内部模型概念,设计了虚拟外部模型,并将所有智能体收敛至其外部模型:文献[12]利用满阶高增益观测器,在相关度不同且无领导者的情况下,得出了异构未知线性多智能体系统的一致性协议。随后在文献[13]的研究中,对文献[12]的系统增加了外部干扰。文献[13]考虑了相关度相同的异构不确定线性多智能体系统,将协同输出看成具有不确定参数的智能体系统的领导跟随一致性问题,即将问题转化为增广矩阵特征值问题,引入一种新的内部模型,结合高增益状态反馈控制技术和分布式技术使其收敛一致。但文献[12-13]没有考虑峰值现象的影响。相对于文献[13],文献[14]考虑了相关度相同的异构未知线性多智能体系统。文献[15]考虑了具有不同未知非线性动力学的多智能体系统的有限时间一致性问题,其中领导智能体的控制输入同样是未知且非线性的,通过将未知非线性动力学参数化,并结合李雅普诺夫函数,提出了一种自适应有限时间协议,在有向网络下,实现领航跟随一致性。   本文采用模型参考控制策略(Model Reference Adaptive Control, MRAC),研究在无向或平衡有向网络下,具有未知参数的异构线性多智能体系统的无领导固定输出平均一致性问题。换言之,本文研究了异构未知线性多智能体系统的一致性问题,网络中的智能体的相关度为1或2。与现有工作相比,本文系统的未知参数的上限是未知的,每个智能体的相关度是不同的,相关度为2的智能体的高频收益是未知的,另外,由于输出的期望值是每个智能体初始输出的平均值,所以相对的放宽了对每个智能体输出的限制。
  1 预备知识和主要问题
  1.1 图论知识
  1.2 符号说明
  4 结语
  本文研究了在无向或平衡有向网络下,具有未知参数的异构线性多智能体系统的固定输出平均一致性问题。基于MRAC方案,提出了一个新的自适应输出一致性协议,实验结果表明,本文协议确保了每个智能体的输出收敛至每个智能体参考模型的输出,即达到了输出平衡平均一致性。对于具有更高相关度、切换拓扑以及有干扰的异构未知线性系统,则是未来工作的挑战。
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