复杂多智能体网络连边正一致性控制与性能分析

Recently, the control and analysis of complex networks based on edge dynamics has drawn a great attention in the control field. The nonnegative edge consensus plays an important role in complex networks that focus on the transmission of nonnegative information. Based on the properties of edge networks and positive systems, this project will present novel methods to study the problems of nonnegative edge consensus, and provide control strategies to achieve optimal convergence performance. We will concentrate on the following aspects: (1) the optimization of the nonnegative edge-consensus with time-delay, design the nonnegative consensus algorithm based on optimization, and improve the existing results with respect to the graph theory, and the main properties of positive systems and edge networks. The relationship between the input time-delay and the convergence rate of optimal nonnegative edge consensus should be established;. (2) the nonnegative edge-consensus problem with undirected topology based on graph filter, the relationship between the nonnegative edge consensus and low-pass filtering should be established. The control strategy with optimal convergence performance will be proposed based on the polynomial implementation of graph filter, and the accurate expression of convergence rate should be constructed; .(3) the nonnegative edge-consensus problem with directed topology based on graph filter, the control strategy with optimal convergence performance and the graph filter will be given based on the polynomial approximation of complex functions. The effect of the topology, the sampling period, and the positive constraint on the convergence rate will be presented. The results will not only further enrich the theory and technology of the distributed cooperation control, but also benefit the application of complex networks in engineering fields, such as social networks, power networks, etc.

近年来，基于连边动力学模型的复杂网络控制与分析成为控制领域的一个研究热点。在侧重非负量传输的网络中，连边动态特性对网络的整体性能、控制与分析具有重要作用。本项目将基于连边网络和正系统的特性，研究复杂多智能体网络连边正一致性问题及实现最优收敛性能的控制策略。重点研究：（1）具有时延的连边正一致优化控制，设计一致优化控制算法，利用图论、正系统和连边网络的特性得到保守性低的收敛条件，给出输入时延与最优正一致收敛率的关系；（2）基于图滤波的无向连边正一致性控制，建立正一致与低通滤波的关联，基于图滤波器多项式实现设计收敛性最优的控制策略，给出精确的收敛率表达式；（3）基于图滤波的有向连边正一致性控制，利用复多项式逼近设计图滤波器和收敛性最优的控制策略，建立拓扑结构、采样周期和正性约束与收敛率的关系。研究结果将进一步丰富和发展分布式协同控制理论与技术，在社交网络、电力网络等工程领域具有重要应用价值。

近年来，基于连边动力学模型的复杂网络控制与分析成为控制领域的一个研究热点。在侧重非负量传输的网络中，连边动态特性对网络的整体性能、控制与分析具有重要作用。本项目将基于连边网络和正系统的特性，研究复杂多智能体网络连边正一致控制理论及实现最优收敛性能的控制策略。.我们取得的主要成果如下：1）研究了基于分布式观测器的节点网络的连边正一致性问题，给出了更优的连边网络Laplacian矩阵非零特征值和一般代数连通度的上下界，与已有文献相比保守性更低，在不需要全局信息的条件下，得到了保守性更低的连边正一致性的充分条件。2）针对带有外部干扰和测量噪声的不确定正多智能体系统，提出了基于区间观测器的分布式控制算法，为正多智能体系统应用于智能电网电压控制奠定了基础。3）针对分布式电池储能系统相同相对State-of-Charge(SoC)变化率的功率分配问题，提出了基于多采样率的连续时间电池储能系统的分布式控制算法，不同于传统连续时间控制方法仅给出平均一致算法的收敛性分析,本文不仅建立了单个控制周期内快速平均一致算法的收敛率表达式,而且给出了包含储能电池动力学和平均一致算法的整个控制系统的渐近稳定性分析.4）提出融合了快速平均一致与多采样率的离散时间控制策略,使各储能电池以相同相对SoC变化率进行充放电.为了仅用局部通信得到计算功率分配值需要的全局平均值,在储能电池拓扑结构已知和未知两种情况下,分别采用了有限时间平均一致算法和具有最优收敛率的平均一致算法.在储能电池单个控制周期内,平均一致算法以小于电池控制周期的采样周期进行多步迭代,从而得到精确的估计值,实现各储能电池的精准功率分配. 所提方法能够更快速、更精准地实现基于相同相对SoC变化率的功率分配.