Journal of Robotics, Networking and Artificial Life
Vol. 5(4); March (2019), pp. 245–248
DOI: https://doi.org/10.2991/jrnal.k.190220.008; ISSN 2405-9021 print; 2352-6386 online
https://www.atlantis-press.com/journals/jrnal

Research Article

Flock Guiding of Hybrid Agents via Root Block
Yunzhong Song*, Ziyi Fu, Fuzhong Wang
Department of Automation, College of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454003, P.R. China

ARTICLE INFO
Article History
Received 15 October 2018
Accepted 29 October 2018

ABSTRACTThe convergent equilibrium of flocking agents is vital importance for their collective behavior, where flock guiding of hybridagents, which are composed by both first and second order agents, can only be boiled down to the root node agents, is touched
upon here. Both the theoretical analysis and the simulation results are provided to verify the suggested scheme.

Keywords
Flock guiding
matrix block
hybrid order agentscollective behavior© 2019 The Authors. Published by Atlantis Press SARL.
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
The collective behavior of agents has been a long and lasting spotlight in systems and control field. The underpinning knowledge
was introduced by Olfati and Murray [1], which including graphtheory, adjacent matrix as well as consensus concepts, made clear
intuitively. Leader follower agent systems, which have been a focus
by many experts, were still being improved up to now. The networksof networks scheme of leader follower systems was made possible
by Song et al. [2], which demonstrating interdependence of agents,
turned into reality via socialized status of the agents. For the engineering complexity, the agents should be different, and only by thisdifference, the engineering systems can function well, and in thiskind of sense, hybrid agents, especially hybrid agents with heterogenous dynamics, were explored in detail. Hybrid agents with both
first and second order dynamics, under auspices of augmented
matrix operation [3], could be assumed unified.
In spite of collective behavior of hybrid agents has been explored so
deeply, there are still some rooms to be filled in. Among those, the ultimate goal of collective behavior will stand out, for its essential value inthe planning of agent goal. Generally speaking, all the members of theagents should contribute and could play their roles, however, counter
intuitively, in this paper, in directed networks of hybrid agents, only theroot block member agents can dominate the final equilibrium of theflock, this is inevitably innovative for agents flocking. And this finding
seems promising in today’s real world, for the authorized agents, their
number should be made as less as possible in case of security.
To be distinguished from the already existed results, our points here
have at least three standing out viewpoints. At first, block guiding
Corresponding author. Email: songhpu@126.com*

which extends the concept of leader guiding in flocking control has
been reported so less often. And secondly, that ultimate goal position is invariant from the leaf block points will be awarded thesedays for security of the networks. And the third, network of hybrid
agents are borrowed to verify the suggested scheme, is much more
promising, for the first order agents can be anchor points sometimes and the second order agents can be the mobile agents, which
will be guided by the anchor agents.
The structure of this paper is arranged as follows. At first, problem
formulation, together with the main results as well as some comments on the main results will be presented in the second part ofthis paper. Then followed that will be some conclusions, which willbe the final part to end up this paper.

2. FLOCK GUIDING OF HYBRID AGENTS
This part will start with the flock guiding of hybrid agents, which
will be covered by Subsection 2.1, the theorem will be demonstrated
at first, and then some notes about it. Then the main results will befollowed at Subsection 2.2, both the topology of the agent networks
and the simulation results will be provided, and after that some comments will be made ready to clarify the idea further in Subsection 2.3.

2.1. Problem Formulation
For the directed networks, which is composed of root block nodes
and leaf block nodes, will be touched upon here. For the root blocknodes, as a whole, they only have output degrees to connect withthe other blocks. Intuitively, the nodes of leaf block, as a whole they
only have input degrees to connect with the other blocks.

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246

Theorem 1. Suppose that the coupling matrix A can be turned into
the following form:
 A 0  , and the row summation of A be zero, D is nonA= 11 B D
singular. And we also assumed the left Eigen vector corresponding toEigen value zero of A be w = [w1 w2]T, then w2 will be vector 0. Andgoing into further, if sub matrix A1 is symmetrical, then, we can get
w = [w1 w2]T = [1, 1, …, 1, 0, …, 0]T
Proof: Since w is the left Eigen vector corresponding to Eigen value
zero of matrix A, then we can get ATw = 0, and this can be translated
into the following Equation (1)
A
0


T
1B   w1 =0DT   w 2 TTo be further, the nodes 1 and 2 are assigned as the first orderagents, while nodes 3–5 are assigned as the second order agents,
respectively.
The coupling matrix of Figure 1 is easily to be gotten as −1 1 0 0 0  1 −1 0 0 0 
A =  1 0 −3 1 1  0 0 1 −1 0 
 0 1 1 1 −3



(1)

The left eigen vector to the zero Eigen value of A isT
1 / 2 1 / 2 0 0 0 , and the dynamics of the system can be
described as Equation (4)(2)

x i = ui , i ∈{1, 2,, n} ;
 x   x x j =  j1  =  j 2  , j ∈{m, m + 1,, N } ; x j 2   u j n = 2, m = n + 1, N = 5.

To be concrete, we can have [Equation (2)]T1 1TA w + B w2 = 0DT w 2 = 0

For D is invertible, w2 must be zero vector. And in this sense, weT
can get A1 w1 = 0, in case of symmetry of A1, we have A1w1 = 0.
Referring that row summation of A1 is zero, so there must exist
vector w1 =[1, 1, , 1]T , that makes Equation (3).
A1w 1 = 0(3)Notes: Theorem 1 points out that if sub-matrix A1 has no input
degrees and is symmetric, then its corresponding nodes can be
named as root nodes and the ultimate state of the networks can bedetermined by those sub block nodes; if sub matrix D is invertible,
and it does not have output degrees connected with the other subblocks, the nodes corresponding to D can be named as leaf nodes,
leaf nodes cannot affect the ultimate state of the networks. So, thedefinition of root nodes together with leaf nodes is the first requisite for system analysis.

2.2. Main Results
Consider the network, which consists of 5 agents, among which
nodes 1 and 2 are root block nodes, while nodes 3–5, are leaf blocknodes, this can be referred to Figure 1.

Figure 1 | Network consists of five nodes.

(4)

which can be ensemble as compact as
0
0

0
0x = 0

0
0
0


0
0
0
0
0
0
0
0

0000
0
0
0
000
1
000
0
0

0
0
0
0
0
0
0
0

0
0
00
1
000

0
0
00
0
0
000
1
00

0
00
0x+00001
0
00
0
100000000010000x = [x1 x2 x31 x32 x 41 x 42
u = [u1 u2 u3 u4 u5 ]T .

x51x52 ]T ,000001000
0
0
0
u0
0
0
1

where

To be concise, the control action can be expressed asa( x2 - x1 )
é u1 ù éùêu ú ê
ú
()axx12
ê 2ú êú
u = ê u3 ú = ê a( x1 + x 41 + x51 - 3x31 ) - bx32 úa(x31 - x 41 ) - bx 42
úê u4 ú êê u5 ú êa(x2 + x 41 + x31 - 3x51 ) - bx ú52 ûë û ë
The introduced control action for agents 1 and 2 are easily to beunderstood, for agents 1 and 2, they make up of the undirected
sub network of root block, and they tend to be convergent to eachother, and this convergent and ultimate value will be assigned to thewhole agents system further. Control action added for agents 3–5
can make a little nervous at first glimpse, but they still can be madetractable in this way, first we decomposed the added control function into two different parts, and the first part is used to realize theconsensus among themselves and their neighbours, and these consensus actions are scaled by proportional factor a, and the second
term is velocity damping part, which is also scaled by proportional
factor, and the scaled value can be varied from a, and in this case
we named the factor as b. The consensus term plus the damping
term collaboratively turn the flock guiding of hybrid agents
possible. Among which, we assigned a = 1 and b = 2, respectively.
The simulation results can be seen in Figure 2.

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3. CONCLUSION
In conclusion, to realize the security of the flock guiding, the ultimate goal of the flock, should be exposed to only several key agents,
and they can be assigned as the root node agents, as to the leafagents, for their popularity is so massive, they should be kept fromthe secrets of the ultimate goal. Flock with secrets keeping is madepossible here with root node and leaf node decomposition.

Figure 2 | Flock guiding of five hybrid agents.

During simulation, the initial values of the agents were listed asfollows
x 0 = [x10 x20 x310 x320 x 410 x 420
x 0 = [3 1 −1 2 3 −2 −2 4]Tx510

x520 ]TFrom Figure 2, the ultimate flock guiding position is 2, it is theaverage of the initial values of agents 1 and 2. So, in this respect,
only the root block agents have their role being played in the ultimate goal of flock guiding. It is much more interesting about thesecond sub variables of agents 3–5, all of them were rendered tozero because of the damped factor of theirs. It seems frustrated
that, the velocity signals of the agents at leaf block are not available sometimes. However, all of the second sub system states canbe observed, it is a standard way to design observers for them. Andin this point, this should not be an excuse to devalue our contribution here. And this is customary, because for the fixed ultimate
goal position, the velocity sub variable must be ceased. Of course,
the ultimate goal can be adjusted if we like, we can regulate theultimate goal position by manipulation the coupling coefficients ofroot block nodes.

2.3. Some Comments
Flock guiding of hybrid agents via root block has its potential
contributions at the following respects: First of all, in the easy
to get and easy to use style of the contemporary network world,
privacy protection problems are becoming more and more pressing, in helps of our idea here, the key information are strongly
suggested to be kept in root block agents. Secondly, infrastructure cyber physical system like smart grid networks, transportation networks, can be kept immune from the injected attacks if
only the small number of the key root block nodes are kept shieldfrom the hackers. And the third, root block agents and leaf block
agents have different dynamics, can conveniently be specified,paired connections of root block nodes and leaf block nodes canbe tagged into block chain, which then strengthened the safety
further. Pros of our suggested scheme are so obvious, and without doubt, we should continue our pursuing to this amazing topic.
And some cons should be overcome in the near future, such as theinjected invaders in the leaf nodes could not change the ultimate
goal position indeed, but they could make the process to the ultimate goal position so difficult, via disturbing the topology of theleaf block agents connected graph. Problems like this one would
be kept as our focus.

System complexity, which is so elusive, could not be easily explained
if we are unwillingly exposed to the concrete systems. The road toclarify the complexity can be made tractable through the following
exemplified engineering systems as well as the theoretical exploration. Instance like high performance vehicle driving, which wasspearheaded in Jia [4] and thereafter individualized designed in Jia[5], can be the justified pilot scale systems. As to the large quantities
complex systems, not only the object itself, but also the endured hostile environment, will be an impediment for the successful manipulation of them. Time varying delays, uncertain and unreliable
information, annoying disturbances, and multi-inputs multi-outputs,
can also be the adversary factors. Adaptive scheme was born to fix
them, and this can be referred to Jia [6]. Reductionism should not
be the only way to deal with the complex system, but it should be
kept in mind at first, for the first step we should know the system
locally in detail to grasp the whole system globally, and in this way,refined analysis and control of the complex systems are necessary.
Refined control of leader follower system according their roles ofthe leader agent, follower agents that have connected path with theleaders, the follower agents that are failed with the connection of
the other agents, and the targeting agent which represent the ultimate goal position are recommended also [7]. So, flock guiding of
hybrid agents via root block, which make the ultimate goal position
invariant even with some adversary leaf agents, will be much morecapable candidate for the robust flocking control of agents system.

ACKNOWLEDGMENTS
This work is partially supported by NSFC Grant (61340041 and61374079) and the Project-sponsored by SRF for ROCS, SEM toYunzhong Song as well as Natural Science Fund of Henan Province(182300410112). The root block and leaf block flock guiding idea isbenefited from the monograph, written by Lu, et al. [8].

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Authors Introduction
Dr. Yunzhong Song

Dr. Fuzhong Wang
He received his PhD from Zhejiang
University, China in 2006. He is a
Professor in the School of ElectricalEngineering and Automation, Henan
Polytechnic University, China. His
main research interests are Multiagent Systems and Complex Networks.

Mr. Ziyi Fu
He is a Professor in the Schoolof Electrical Engineering andAutomation, Henan PolytechnicUniversity, China. His main researchinterests are electrical drive systemand system integration, especially
fault detection and diagnosis.

He is a Professor and also the Executive
Dean of the School of ElectricalEngineering and Automation, Henan
Polytechnic University, China. His
main research interests are powersystem transmission and control,
process control especially fault detection and diagnosis.