CN103869698A

CN103869698A - Sampling control method of multi-intellectual body system consistency

Info

Publication number: CN103869698A
Application number: CN201210551784.8A
Authority: CN
Inventors: 彭力; 王娜
Original assignee: Jiangnan University
Current assignee: Jiangnan University
Priority date: 2012-12-18
Filing date: 2012-12-18
Publication date: 2014-06-18

Abstract

The invention belongs to the field of intelligent control and provides a sampling control method of multi-intellectual body system consistency. By using delay decomposition technology, the invention provides a novel consistency algorithm, i.e. a sampling control protocol of first-order multi-intellectual body system consistency with delay state derivative feedback. Based on the study on sampling data control, an appropriate sampling period is searched by using a stability theory and an algebraic graph theory of a linear system, and the necessary and sufficient conditions of gradually realizing average consistency of the first-order multi-intellectual body system consistency with the delay state derivative feedback are respectively discussed. The method has the advantages that the original protocol of a delay state derivative which is approximately calculated by using numerical differentiation is substituted, the appropriate sampling period is selected to ensure the realization of the consistency, and the necessary and sufficient conditions of gradually realizing the average consistency of the first-order multi-intellectual body system consistency with the delay state derivative feedback are respectively discussed, so that the stability of the system is improved.

Description

A Sampling Control Method for Consistency in Multi-agent Systems

一、技术领域1. Technical field

本发明是多智能体系统一致性的采样控制方法，属于智能控制领域。The invention is a consistent sampling control method for multi-agent systems, belonging to the field of intelligent control.

二、背景技术2. Background technology

多智能体系统是近年来发展起来的一门新兴的复杂系统科学，同时它也是一门涉及生物、数学、物理、控制、计算机、通信以及人工智能的综合性交叉学科。目前多智能体系统的协调控制问题已经得到来自这些领域的科研工作者的广泛关注。Multi-agent system is an emerging complex system science developed in recent years, and it is also a comprehensive interdisciplinary subject involving biology, mathematics, physics, control, computer, communication and artificial intelligence. At present, the problem of coordinated control of multi-agent systems has received extensive attention from researchers in these fields.

我们对多智能体系统的分布式协同控制进行研究，不仅仅是为了揭示自然界中许多物理现象的内在规律，更重要的是利用所获得的对其内在规律的认识更好地指导我们的活动，更好地服务于人类社会。如今，多智能体系统的分布式协同控制已经应用到许多领域，如群集、聚集、蜂拥、编队控制、分布式传感器网络、通信网络的拥塞控制、无人驾驶航空器的协同控制及姿态协调等等。Our research on the distributed cooperative control of multi-agent systems is not only to reveal the internal laws of many physical phenomena in nature, but more importantly, to use the obtained understanding of its internal laws to better guide our activities. better serve the human society. Today, distributed cooperative control of multi-agent systems has been applied to many fields, such as swarming, gathering, swarming, formation control, distributed sensor networks, congestion control of communication networks, cooperative control and attitude coordination of unmanned aircraft, etc. .

在实际中，用多智能体系统取代目前的人工操作系统可以很大程度的节省生产成本，并且更加安全；此外，群体通过局部协作而获得群体优势的特点也刺激了多智能体系统在工程中的应用。在军事领域，采用空中无人驾驶机系统进行作战和侦察，可以减少人员的伤亡，还能具有超高过载的机动能力，有利于攻击和摆脱威胁；在民用领域，多智能体系统可以完成资源勘测、灾情侦察、通信中继、环境监测等繁重、重复或具有一定危险性的任务，例如自治移动小车系统，自动高速公路系统，空间开发与探测，海洋勘探，传感器网络等。而且，据专家们推测，“21世纪可能成为无人战争时代”，也就是说，未来战场上自动化技术将得到大规模的运用，各种自治的和半自治的地面、空中和海上的作战平台将通过多智能体系统联系在一起，与作战人员共同完成任务，这将是一种无可争议的发展趋势。In practice, replacing the current artificial operating system with a multi-agent system can greatly save production costs and be safer; in addition, the characteristics of groups gaining group advantages through local cooperation also stimulate the use of multi-agent systems in engineering. Applications. In the military field, the use of aerial unmanned aerial vehicle systems for combat and reconnaissance can reduce casualties, and it can also have ultra-high overload maneuverability, which is conducive to attacking and getting rid of threats; in the civilian field, multi-agent systems can complete resources. Heavy, repetitive or dangerous tasks such as surveying, disaster reconnaissance, communication relay, and environmental monitoring, such as autonomous mobile car systems, automatic highway systems, space development and detection, ocean exploration, sensor networks, etc. Moreover, according to experts' speculation, "the 21st century may become an era of unmanned warfare", that is to say, automation technology will be used on a large scale in the future battlefield, and various autonomous and semi-autonomous ground, air and sea combat platforms It will be an indisputable development trend to link together through a multi-agent system and complete tasks with combatants.

三、发明内容3. Contents of the invention

本发明的目的在于提出了多智能体系统一致性的采样控制方法。具体实现包括以下内容：The purpose of the present invention is to propose a sampling control method for multi-agent system consistency. The specific implementation includes the following:

在实际应用中，通信时滞(主要是个体之间通过传感器或通信设备进行信息传输而产生的)和输入时滞(个体自身对于外部作用或信号的处理所产生的)的干扰是不可避免的，而且可能引起网络系统的发散或震荡。因此，对时滞影响的研究是十分必要的。In practical applications, the interference of communication time lag (mainly caused by information transmission between individuals through sensors or communication devices) and input time lag (generated by the individual's own processing of external effects or signals) is inevitable. , and may cause divergence or oscillation of the network system. Therefore, research on the effect of time lag is very necessary.

由于通讯条件的限制和总成本约束，信息几乎不能连续传递，或者只能周期性交换信息.另一方面，在很多情形下，尽管系统本身是一个连续时间过程，但是由于数字传感器和控制器的应用，在许多情况下，尽管系统本身是一个连续过程，但是控制器的综合仅使用采样时刻的信息，即只有在离散采样瞬间的采样数据对控制合成有效。所以，考虑间歇性传输信息更加实用，从而建模为离散时间系统或混合系统。与带有连续时间控制器的连续时间系统或自身就是离散时间的系统相比，通过采样控制的连续时间系统有许多优点。一方面，基于采样数据设计的数字控制器在控制精度、控制速度、控制性能以及控制费用方面具有明显优势。另一方面，在工程应用中，连续信号对通信带宽的要求更高，这在大多数情况下是不可得到的。因此，连续时间系统的采样控制更能满足实际情况的需要。Due to the limitations of communication conditions and total cost constraints, information can hardly be transmitted continuously, or information can only be exchanged periodically. On the other hand, in many cases, although the system itself is a continuous time process, due to the digital sensor and controller In many cases, although the system itself is a continuous process, the synthesis of the controller only uses the information at the sampling instant, that is, only the sampling data at discrete sampling instants are valid for the control synthesis. Therefore, it is more practical to consider the intermittent transfer of information and thus model it as a discrete-time system or as a hybrid system. A continuous-time system controlled by sampling has many advantages over a continuous-time system with a continuous-time controller or a system that is itself discrete-time. On the one hand, the digital controller designed based on sampling data has obvious advantages in control accuracy, control speed, control performance and control cost. On the other hand, in engineering applications, continuous signals have higher requirements on communication bandwidth, which is unavailable in most cases. Therefore, the sampling control of the continuous time system can better meet the needs of the actual situation.

对于大多数现有的一致性协议，大部分是在当前状态或时滞存在下提出的。然而，在某些情况下，时滞状态导数反馈的引入在确保系统实现一致性方面是非常有必要的。2011年曹等人研究了具有时变参考状态的一阶和二阶连续时间多智能体系统的一致性跟踪问题并证明了当虚拟领导仅对部分智能体存在时，提出的不具有时滞状态导数反馈的一致性跟踪协议不能确保实现一致性的跟踪。同时，2012年吴等人在具有通信时滞的连续时间多智能体系统中，通过引入适当的时滞状态导数反馈增益，提高了一致性的性能，其性能主要包括通信时滞的鲁棒性(即系统所能容忍的最大时滞)和实现一致的收敛速度。然而，曹和吴的研究在实际应用中，对于某个智能体很难获得它的邻居智能体的时滞状态导数反馈信息，就是说具有时滞状态导数反馈的一致性很难实现。为了克服这个问题，2012年吴等人提出了采样数据控制条件下使用数值微分来近似计算时滞状态导数的策略，然而，这种近似计算可能破坏系统的稳定性。而且，文献中选取适当的采样周期来确保一致性的实现目前还没有被引用。For most existing consensus protocols, most are proposed in the presence of current state or time lag. However, in some cases, the introduction of time-delay state derivative feedback is very necessary in ensuring that the system achieves consistency. In 2011, Cao et al. studied the consistency tracking problem of first-order and second-order continuous-time multi-agent systems with time-varying reference states and proved that when the virtual leader only exists for some agents, the proposed state without time-delay A consistent tracking protocol for derivative feedback does not ensure consistent tracking. At the same time, in 2012, in a continuous-time multi-agent system with communication time-delay, Wu et al. improved the consistency performance by introducing an appropriate time-delay state derivative feedback gain, and its performance mainly includes the robustness of communication time-delay (that is, the maximum time delay that the system can tolerate) and achieve a consistent convergence rate. However, in the practical application of Cao and Wu's research, it is difficult for an agent to obtain the time-delay state derivative feedback information of its neighbor agents, that is to say, the consistency of time-delay state derivative feedback is difficult to achieve. In order to overcome this problem, in 2012 Wu et al. proposed a strategy of using numerical differentiation to approximate the time-delay state derivatives under sampled data control conditions. However, this approximate calculation may destroy the stability of the system. Moreover, implementations in the literature for choosing an appropriate sampling period to ensure consistency have not been cited so far.

综合以上分析，主要从以下几个方面进行研究：Based on the above analysis, the research is mainly carried out from the following aspects:

(1)应用时滞分解技术，提出了一种新的一致性算法即具有时滞状态导数反馈的一阶多智能体系统一致性的采样控制协议；(1) Applying time-delay decomposition technology, a new consensus algorithm is proposed, which is a first-order multi-agent system consensus sampling control protocol with time-delay state derivative feedback;

(2)基于采样数据控制的研究，应用线性系统的稳定性理论和代数图论，寻找适当的采样周期，分别讨论了具有时滞状态导数反馈的一阶多智能体系统实现一致性的充分必要条件；(2) Based on the study of sampling data control, applying the stability theory of linear systems and algebraic graph theory to find an appropriate sampling period, discussing the necessity and sufficiency of achieving consistency in first-order multi-agent systems with time-delay state derivative feedback condition;

(3)数值仿真图证明了理论结果的有效性。(3) Numerical simulation diagrams prove the effectiveness of the theoretical results.

本发明的优点在于取代原有的使用数值微分来近似计算时滞状态导数的协议，选取适当的采样周期来确保一致性的实现，从而提高了系统的稳定性。The advantage of the present invention is that it replaces the original protocol that uses numerical differentiation to approximate the time-delay state derivative, and selects an appropriate sampling period to ensure the realization of consistency, thereby improving the stability of the system.

附图说明 Description of drawings

图1为本发明中使用的由四个智能体构成的加权无向连通的网络拓扑结构图；Fig. 1 is the network topology structure figure of the weighted undirected connection that uses among the present invention to be formed by four agents;

图2多智能体系统稳定的状态图；Figure 2 is a stable state diagram of the multi-agent system;

图3多智能体系统不稳定的状态图。Figure 3. The state diagram of multi-agent system instability.

具体实施方式：Detailed ways:

下面结合附图和具体实例对本发明做进一步说明：Below in conjunction with accompanying drawing and specific example the present invention will be further described:

a)问题描述：a) Problem description:

结合附图1，考虑如下一阶多智能体系统

i∈I (1)Combined with Figure 1, consider the following first-order multi-agent system

i∈I (1)

其中，x_i(t)∈R和u_i(t)∈R分别代表智能体i的状态和相应的控制输入。where x _i (t) ∈ R and u _i (t) ∈ R represent the state of agent i and the corresponding control input, respectively.

定义1多智能体系统(1)被称为渐近实现平均一致，如果每个智能体的状态满足渐近性：

为了同时提高通信时滞的鲁棒性和实现一致的收敛速度，吴和方提出了以下基于时滞状态导数反馈的一致性协议：Definition 1 A multi-agent system (1) is said to asymptotically achieve mean consistency if the state of each agent satisfies asymptotically:

To simultaneously improve the robustness of communication time-delays and achieve a consistent convergence rate, Wu and Fang proposed the following consensus protocol based on time-delay state derivative feedback:

${μ μ}_{i i} ((t t)) = = \underset{j j &Element; &Element; {N N}_{i i}}{Σ Σ} {a a}_{ij ij} {{[[{x x}_{j j} ((t t - - τ τ)) + + β β {\overset{\cdot \cdot}{x x}}_{j j} ((t t - - τ τ))]] - - [[{x x}_{i i} ((t t - - τ τ)) + + β β {\overset{\cdot &Center Dot;}{x x}}_{i i} ((t t - - τ τ))]]}} - - - - - - ((22))$

其中，τ＞0代表通信时滞和β代表时滞状态导数反馈的强度并满足β∈(0，min{τ，1/λ_N(L)}).Among them, τ>0 represents the communication delay and β represents the strength of the time-delay state derivative feedback and satisfies β∈(0, min{τ, 1/λ _N (L)}).

为了应用协议(2)使多智能体系统实现一致性，我们提出了一种新的方法即，使用(x_i(t-τ)-x_i(t-τ-h))/h和(x_j(t-τ)-x_j(t-τ-h))/h，j∈N_i来分别代替

和x_j(t-τ)，j∈N_i。其中，h＞0代表采样周期。于是我们就提出了具有时滞状态导数反馈的一阶多智能体系统一致性的数值微分的协议：In order to apply protocol (2) to achieve consensus in multi-agent systems, we propose a new method that uses ( _xi (t-τ) _-xi (t-τ-h))/h and (x _j (t-τ)-x _j (t-τ-h))/h, j∈N _i to replace

and x _j (t-τ), j∈N _i . Among them, h>0 represents the sampling period. We then propose a protocol for the numerical differentiation of consensus in first-order multi-agent systems with time-delay state derivative feedback:

${u u}_{i i} ((t t)) = = \underset{j j &Element; &Element; {N N}_{i i}}{Σ Σ} {a a}_{ij ij} {{[[{x x}_{j j} ((t t - - τ τ)) + + β β (({x x}_{j j} ((t t - - τ τ)) - - {x x}_{j j} ((t t - - τ τ - - h h)))) / / h h]] - - [[{x x}_{i i} ((t t - - τ τ)) + + β β (({x x}_{i i} ((t t - - τ τ)) - - {x x}_{i i} ((t t - - τ τ - - h h)))) / / h h]]}} . . - - - - - - ((33))$

对通信时滞τ关于采样周期h进行时滞分解得：τ＝mh+ε(4)Decompose the communication time delay τ with respect to the sampling period h: τ=mh+ε(4)

其中，m非负整数和ε∈[0，h)。where m is a non-negative integer and ε∈[0,h).

使用周期采样技术和零阶保持器技术，由一致性协议(3)我们提出了具有时滞状态导数反馈的一阶多智能体系统一致性的采样控制协议：Using the periodic sampling technique and the zero-order keeper technique, we propose a sampling control protocol for first-order multi-agent system consensus with time-delay state derivative feedback from the consensus protocol (3):

${u u}_{i i} ((t t)) = = \{\begin{matrix} {u u}_{i i} ((kh kh - - mh m h - - h h)) = = \underset{j j &Element; &Element; {N N}_{i i}}{Σ Σ} {a a}_{ij ij} {{[[{x x}_{j j} ((kh kh - - mh m h - - h h)) + + β β (({x x}_{j j} ((kh kh - - mh m h - - h h)) - - {x x}_{j j} ((kh kh - - mh m h - - 22 h h)))) / / h h]] \\ - - [[{x x}_{i i} ((kh kh - - mh m h - - h h)) + + β β (({x x}_{i i} ((kh kh - - mh m h - - h h)) - - {x x}_{i i} ((kh kh - - mh m h - - 22 h h)))) / / h h]]}},, t t &Element; &Element; [[kh kh,, kh kh + + ϵ ϵ));; \\ {u u}_{i i} ((kh kh - - mh m h)) = = \underset{j j &Element; &Element; {N N}_{i i}}{Σ Σ} {a a}_{ij ij} {{[[{x x}_{j j} ((kh kh - - mh m h)) + + β β (({x x}_{j j} ((kh kh - - mh m h)) - - {x x}_{j j} ((kh kh - - mh m h - - h h)))) / / h h]] \\ - - [[{x x}_{i i} ((kh kh - - mh m h)) + + β β (({x x}_{j j} ((kh kh - - mh m h)) - - {x x}_{j j} ((kh kh - - mh m h - - h h)))) / / h h]]}},, t t &Element; &Element; [[kh kh + + ϵ ϵ,, kh kh + + h h)) . . \end{matrix} - - - - - - ((55))$

我们说系统(1)渐近实现了平均一致性，当

We say that system (1) asymptotically achieves average consistency when

引理1方程s³+a₂s²+a₁s+a₀＝0的所有根都在单位圆内，其中a₂，a₁，a₀∈R，当且仅当下面四个不等式1+a₂+a₁+a₀＞0，-1+a₂-a₁+a₀＜0，|a₀|＜1和|a₀ ²-1|＞|a₀a₂-a₁|同时成立。Lemma 1 All roots of the equation s ³ +a ₂ s ² +a ₁ s+a ₀ =0 are in the unit circle, where a ₂ , a ₁ , a ₀ ∈ R, if and only if the following four inequalities 1 +a ₂ +a ₁ +a ₀ >0, -1+a ₂ -a ₁ +a ₀ <0, |a ₀ |<1 and |a ₀ ² -1|>|a ₀ a ₂ -a ₁ | established at the same time.

b)收敛性分析b) Convergence analysis

在这部分中，应用线性系统的稳定性理论和代数图论等知识，我们得到了确保多智能体系统(1)应用一致性协议(5)实现平均一致性的充分必要条件，即方程In this part, applying the knowledge of the stability theory of linear systems and algebraic graph theory, we obtain the sufficient and necessary conditions to ensure that the multi-agent system (1) applies the consensus protocol (5) to achieve average consistency, that is, the equation

z^m+3-z^m+2+(h-ε)(1+β/h)λ_i(L)z²+(ε-β+2εβ/h)λ_i(L)z-ε(β/h)λ_i(L)＝0，i∈I\{1}(6)z ^m+3 -z ^m+2 +(h-ε)(1+β/h)λ _i (L)z ² +(ε-β+2εβ/h)λ _i (L)z-ε(β/ h) λ _i (L) = 0, i∈I\{1} (6)

的所有根都在单位圆内。All roots of are inside the unit circle.

尽管方程(6)所有根都在单位圆内是充分必要条件，但对于大采样时滞，很难得到确保多智能体系统(1)应用一致性协议(5)实现平均一致性的精确地采样周期的取值范围。因此，方程(6)的理论结果主要用来测试确保实现一致性的采样周期的有效性。Although it is a necessary and sufficient condition for all roots of equation (6) to be within the unit circle, for large sampling delays, it is difficult to obtain an accurate sampling that ensures that the multi-agent system (1) applies the consensus protocol (5) to achieve average consistency The value range of the period. Therefore, the theoretical results of equation (6) are mainly used to test the effectiveness of the sampling period to ensure that consistency is achieved.

由时滞分解技术方程(4)可以得出，当m＝0和ε≠0时，0＜ε＝τ＜h，也就是说通信时滞要小于采样周期。在这种情况下，带有大采样时滞的一致性协议(5)退化为带有小采样时滞的一致性协议： $u_{i} (t) = \{\begin{matrix} u_{i} (kh - h) = \underset{j &Element; N_{i}}{Σ} a_{ij} {[x_{j} (kh - h) + β (x_{j} (kh - h) - x_{j} (kh - 2 h)) / h] \\ - [x_{i} (kh - h) + β (x_{i} (kh - h) - x_{i} (kh - 2 h)) / h]}, t &Element; [kh, kh + τ); \\ u_{i} (kh) = \underset{j &Element; N_{i}}{Σ} a_{ij} {[x_{j} (kh) + β (x_{j} (kh) - x_{j} (kh - h)) / h] \\ - [x_{i} (kh) + β (x_{j} (kh) - x_{j} (kh - h)) / h]}, t &Element; [kh + τ, kh + h) . \end{matrix} - - - (7)$ From the time-delay decomposition technical equation (4), it can be concluded that when m=0 and ε≠0, 0<ε=τ<h, that is to say, the communication time-lag is smaller than the sampling period. In this case, the consensus protocol (5) with a large sampling delay degenerates into a consensus protocol with a small sampling delay: $u_{i} (t) = \{\begin{matrix} u_{i} (kh - h) = \underset{j &Element; N_{i}}{Σ} a_{ij} {[x_{j} (kh - h) + β (x_{j} (kh - h) - x_{j} (kh - 2 h)) / h] \\ - [x_{i} (kh - h) + β (x_{i} (kh - h) - x_{i} (kh - 2 h)) / h]}, t &Element; [kh, kh + τ); \\ u_{i} (kh) = \underset{j &Element; N_{i}}{Σ} a_{ij} {[x_{j} (kh) + β (x_{j} (kh) - x_{j} (kh - h)) / h] \\ - [x_{i} (kh) + β (x_{j} (kh) - x_{j} (kh - h)) / h]}, t &Element; [kh + τ, kh + h) . \end{matrix} - - - (7)$

结合附图1，考虑到多智能体系统(1)具有一个固定的，无向的，连通的网络拓扑结构。假定τ＜1/λ_N，那么多智能体系统(1)应用一致性协议(7)实现了平均一致性，当且仅当With reference to Figure 1, it is considered that the multi-agent system (1) has a fixed, undirected, connected network topology. Assuming τ<1/λ _N , then the multi-agent system (1) achieves average consensus by applying the consensus protocol (7), if and only if

$max max {{τ τ,, \frac{βτ βτ {λ λ}_{N N} ((11 - - τ τ {λ λ}_{N N} + + β β {λ λ}_{N N}))}{((11 + + β β {λ λ}_{N N})) ((11 - - τ τ {λ λ}_{N N}))}}} < < h h < < \sqrt{{((β β - - τ τ - - 11 / / {λ λ}_{N N}))}^{22} + + 44 βτ βτ} + + τ τ + + 11 / / {λ λ}_{N N} - - β β . . - - - - - - ((88))$

证明：当0＜ε＝τ＜h，方程(6)退化为Proof: when 0<ε=τ<h, equation (6) degenerates into

z³+[(h-τ)(1+β/h)λ_i(L)-1]z²+(τ-β+2τβ/h)λ_i(L)z-τ(β/h)λ_i(L)＝0，i ∈I\{1}.(9)z ³ +[(h-τ)(1+β/h)λ _i (L)-1]z ² +(τ-β+2τβ/h)λ _i (L)z-τ(β/h)λ _i (L)=0, i ∈ I\{1}.(9)

由引理1，方程(9)的所有根都在单位圆内当且仅当By Lemma 1, all roots of equation (9) lie in the unit circle if and only if

$\{\begin{matrix} h h {λ λ}_{i i} ((L L)) > > 00;; \\ ((h h + + 22 β β - - 22 τ τ - - 44 τβ τβ / / h h)) {λ λ}_{i i} ((L L)) < < 22;; \\ τ τ ((β β / / h h)) {λ λ}_{i i} ((L L)) < < 11;; \\ | | {τ τ}^{22} (({β β}^{22} / / {h h}^{22})) {λ λ}_{i i}^{22} ((L L)) - - 11 | | > > \\ | | [[((h h - - τ τ)) ((11 + + β β / / h h)) {λ λ}_{i i} ((L L)) - - 11]] τ τ ((β β / / h h)) {λ λ}_{i i} ((L L)) \\ - - ((τ τ - - β β + + 22 τβ τβ / / h h)) {λ λ}_{i i} ((L L)) | | \end{matrix},, i i &Element; &Element; I I \ \ {{11]] . . - - - - - - ((1010))$

证明完成。The proof is complete.

c)实验仿真结果c) Experimental simulation results

结合附图1，很容易得到L的最大特征值λ₄为4。本算法以采样周期为例做仿真实验，现假设τ＝0.2和β＝0.1，由(8)得出了确保多智能体系统(1)应用一致性协议(7)实现平均一致性的采样周期的取值范围是(0.2，0.8)。Combined with accompanying drawing 1, it is easy to obtain that the largest eigenvalue λ ₄ of L is 4. This algorithm takes the sampling period as an example to do the simulation experiment. Assuming τ=0.2 and β=0.1, the sampling period to ensure the average consistency of the multi-agent system (1) and (7) is obtained from (8) The value range of is (0.2, 0.8).

结合附图2，我们发现当h＝0.3时，满足(8)的条件，给定的多智能体系统(1)应用一致性协议(7)实现了平均一致性。Combining with Figure 2, we find that when h=0.3, the condition of (8) is met, and the given multi-agent system (1) implements the average consistency by applying the consensus protocol (7).

结合附图3，我们发现当h＝0.9时，满足(8)的条件，给定的多智能体系统(1)应用一致性协议(7)不能实现平均一致性。Combined with Fig. 3, we found that when h=0.9, the condition of (8) is met, and the given multi-agent system (1) cannot achieve the average consensus by applying the consensus protocol (7).

Claims

1. the conforming sampling control method of multi-agent system, the method is mainly studied from the following aspects:

(1) application time lag decomposition technique, has proposed a kind of new consistency algorithm and has had the conforming controlling of sampling agreement of single order multi-agent system of time lag state derivative feedback;

(2) research based on sampled data control, stability theory and the algebraic graph theory of application linear system, find the suitable sampling period, the progressive sufficient and necessary condition of realizing average homogeneity of single order multi-agent system with time lag state derivative feedback has been discussed respectively;

(3) numerical simulation figure has proved the validity of notional result.

2. the conforming sampling control method of multi-agent system according to claim 1, is characterized in that: the time lag decomposition technique theory in described content (1) proposition and a kind of new consistency algorithm proposed had the conforming controlling of sampling agreement of single order multi-agent system of time lag state derivative feedback.

3. the conforming sampling control method of multi-agent system according to claim 1, it is characterized in that: described step (2) is being utilized stability theory and the algebraic graph theory of linear system, find the suitable sampling period, the progressive sufficient and necessary condition of realizing average homogeneity of single order multi-agent system with time lag state derivative feedback has been discussed respectively.