Li Ma 2024a - Revision history

Rimni at 11:47, 21 June 2024

2024-06-21T11:47:54Z

Rimni at 11:47, 21 June 2024

2024-06-21T11:47:01Z

Rimni at 11:36, 21 June 2024

2024-06-21T11:36:38Z

Rimni: /* References */

2024-06-21T11:35:13Z

‎References

Rimni: /* 1. Introduction */

2024-06-21T11:33:35Z

‎1. Introduction

Rimni at 11:27, 21 June 2024

2024-06-21T11:27:24Z

Rimni: /* 3.2 Numerical simulation */

2024-06-21T10:37:40Z

‎3.2 Numerical simulation

Rimni at 10:35, 21 June 2024

2024-06-21T10:35:30Z

Rimni at 10:30, 21 June 2024

2024-06-21T10:30:33Z

Rimni at 10:15, 21 June 2024

2024-06-21T10:15:02Z

@@ Line 299: / Line 299: @@
 To validate the correctness and effectiveness of the theoretical results proposed in this study, numerical simulations are conducted using two numerical examples. The details are as follows:
-From the theoretical results, it is known that a one-dimensional fractional-order switching complex network formed by three nodes is considered. Assuming the initial moment <math display="inline"> t_0 </math> is set to 0, <math display="inline">  apha</math> is set to 0.8, and the function <math display="inline"> f </math> is set to 0.3. It is also assumed that the network has three communication topologies, which are labeled and presented graphically as shown in [[#img-1|Figure 1]].
+From the theoretical results, it is known that a one-dimensional fractional-order switching complex network formed by three nodes is considered. Assuming the initial moment <math display="inline"> t_0 </math> is set to 0, <math display="inline">  \alpha</math> is set to 0.8, and the function <math display="inline"> f </math> is set to 0.3. It is also assumed that the network has three communication topologies, which are labeled and presented graphically as shown in [[#img-1|Figure 1]].
 <div id='img-1'></div>

@@ Line 46: / Line 46: @@
 ===2.3 Design of models and controllers===
-First, in terms of model design, consider a Caputo fractional-order complex network with switching topology composed of multiple nodes. All communication topology can be designed as a finite set of undirected graphs, denoted as <math>\left\{G^1\left(V,\varepsilon^1,\xi^1\right),...,G^n\left(V,\varepsilon^n,\xi^n\right)\right\}</math>, where the first item in the set <math display="inline">(V)</math> is a collection of all network nodes, expressed as <math display="inline">V=v_1, v_2,v_3,\ldots ,v_n</math>, <math>\varepsilon^n</math> represents the set of undirected edges for the <math display="inline">n  </math><sup>th</sup> topology, <math display="inline">\zeta^n</math> is the adjacency matrix for the <math display="inline"> n</math><sup>th</sup> topology graph, <math display="inline">n</math> being a natural number. For clarity, <math display="inline">G^n</math> be represented as <math display="inline">G^n (V, \varepsilon^n, \zeta^n)</math>. Also, represent the nodes <math display="inline">(v_i,v_j)</math> as the edges between nodes, and define the elements in the matrix <math display="inline">\zeta^n</math>. The formula is as follows:
+First, in terms of model design, consider a Caputo fractional-order complex network with switching topology composed of multiple nodes. All communication topology can be designed as a finite set of undirected graphs, denoted as <math>\left\{G^1\left(V,\varepsilon^1,\xi^1\right),...,G^n\left(V,\varepsilon^n,\xi^n\right)\right\}</math>, where the first item in the set <math display="inline">(V)</math> is a collection of all network nodes, expressed as <math display="inline">V=v_1, v_2,v_3,\ldots ,v_n</math>, <math>\varepsilon^n</math> represents the set of undirected edges for the <math display="inline">n  </math><sup>th</sup> topology, <math display="inline">\zeta^n</math> is the adjacency matrix for the <math display="inline"> n</math><sup>th</sup> topology graph, <math display="inline">n</math> being a natural number. For clarity, <math display="inline">G^n</math> be represented as <math display="inline">G^n (V, \varepsilon^n, \zeta^n)</math>. Also, represent the nodes <math display="inline">(v_i,v_j)</math> as the edges between nodes, and define the elements in the matrix <math display="inline">\zeta^n</math>. The equation is as follows:
 {| class="formulaSCP" style="width: 100%; text-align: left;"

@@ Line 28: / Line 28: @@
 In a similar vein, Ma et al. [8] ventured into the realm of topology identification for fractional-order complex networks, employing a strategy of variable substitution control. By devising a response network predicated on this control mechanism and a concurrent parameter update law, they derived a set of criteria for achieving both topology identification and network synchronization, with numerical simulations serving as a testament to the method’s validity. Collectively, these scholarly endeavors within the domains of switching topology and fractional-order complex networks not only enrich theoretical discourse but also chart a definitive course for empirical inquiry.
-In the realm of global research on switching topology and fractional-order complex networks, Ding et al. [9] have probed the intricacies of complex modified projective synchronization (CMPS) and the parameter estimation within time-varying coupled fractional-order complex-valued dynamic networks (FOCDN). Their theoretical discourse posits that FOCDN, when faced with time-varying delays, can attain CMPS via adaptive controllers—a premise substantiated by two numerical exemplars within the complex-valued domain, thereby affirming the potency of the refined projection strategy for fractional-order complex networks. Concurrently, Du et al. [10] have delved into the delay-dependent finite-time synchronization (FTS) criterion pertinent to a subset of fractional-order delay complex networks (FODCNs). By leveraging the Young inequality and the rules governing fractional-order derivatives of composite functions, they unveiled a novel delay-dependent fractional-order finite-time convergence principle (FOFTCP), wherein the stability duration is contingent upon the temporal delay. This newly minted FOFTCP, in concert with a meticulously crafted feedback controller, has yielded a fresh FTS criterion for FODCNs, the efficacy of which has been corroborated through two numerical demonstrations. In a parallel vein, Behinfaraz Behinfaraz and Ghaemi [11] have embarked on an exploration of the identification and synchronization within fractional-order complex networks, characterized by switching topology and time-variant delays, through the lens of fuzzy methodologies. The dynamics of the network nodes, deemed chaotic, were instantiated via a circuit realization tailored to these time-delay fractional-order dynamics. Employing T-S fuzzy modeling, they introduced an innovative representational paradigm for fractional-order chaotic systems, with simulations and empirical outcomes underscoring the proposed method's performance. Selvaraj  et al. [12] scrutinized the cluster synchronization and the mitigation of disturbances within fractional-order complex networks, beset by coupling delays, unknown uncertainties, and disturbances (UDs). A modified repetitive control (MRC) block was seamlessly integrated into a closed-loop feedback control circuit to tackle these challenges. Furthermore, they formulated a comprehensive suite of sufficient linear matrix inequality constraints to guarantee the system's cluster synchronization. The merits, practicability, and resilience of the MRC framework, predicated on UDE, were validated through two illustrative cases. This overview elucidates that international research endeavors in switching topology and fractional-order complex networks are markedly more focused than their domestic counterparts, thereby serving as a repository of valuable insights and benchmarks for domestic scholarly pursuits in these spheres.
+In the realm of global research on switching topology and fractional-order complex networks, Ding et al. [9] have probed the intricacies of complex modified projective synchronization (CMPS) and the parameter estimation within time-varying coupled fractional-order complex-valued dynamic networks (FOCDN). Their theoretical discourse posits that FOCDN, when faced with time-varying delays, can attain CMPS via adaptive controllers—a premise substantiated by two numerical exemplars within the complex-valued domain, thereby affirming the potency of the refined projection strategy for fractional-order complex networks. Concurrently, Du et al. [10] have delved into the delay-dependent finite-time synchronization (FTS) criterion pertinent to a subset of fractional-order delay complex networks (FODCNs). By leveraging the Young inequality and the rules governing fractional-order derivatives of composite functions, they unveiled a novel delay-dependent fractional-order finite-time convergence principle (FOFTCP), wherein the stability duration is contingent upon the temporal delay. This newly minted FOFTCP, in concert with a meticulously crafted feedback controller, has yielded a fresh FTS criterion for FODCNs, the efficacy of which has been corroborated through two numerical demonstrations. In a parallel vein, Behinfaraz and Ghaemi [11] have embarked on an exploration of the identification and synchronization within fractional-order complex networks, characterized by switching topology and time-variant delays, through the lens of fuzzy methodologies. The dynamics of the network nodes, deemed chaotic, were instantiated via a circuit realization tailored to these time-delay fractional-order dynamics. Employing T-S fuzzy modeling, they introduced an innovative representational paradigm for fractional-order chaotic systems, with simulations and empirical outcomes underscoring the proposed method's performance. Selvaraj  et al. [12] scrutinized the cluster synchronization and the mitigation of disturbances within fractional-order complex networks, beset by coupling delays, unknown uncertainties, and disturbances (UDs). A modified repetitive control (MRC) block was seamlessly integrated into a closed-loop feedback control circuit to tackle these challenges. Furthermore, they formulated a comprehensive suite of sufficient linear matrix inequality constraints to guarantee the system's cluster synchronization. The merits, practicability, and resilience of the MRC framework, predicated on UDE, were validated through two illustrative cases. This overview elucidates that international research endeavors in switching topology and fractional-order complex networks are markedly more focused than their domestic counterparts, thereby serving as a repository of valuable insights and benchmarks for domestic scholarly pursuits in these spheres.
 ==2. Research content==

@@ Line 432: / Line 432: @@
 [10] Du F., Lu J.G., Zhang Q.H.. Delay-dependent finite-time synchronization criterion of fractional-order delayed complex networks. Communications in Nonlinear Science and Numerical Simulation, 119, 107072, 2023.
-[11] Reza B., Sehraneh G. Identification and synchronization of switching fractional-order complex networks with time-varying delays based on a fuzzy method. International Journal of Fuzzy Systems, 24(5):2203-2214, 2022.
+[11] Behinfaraz R., Ghaemi S. Identification and synchronization of switching fractional-order complex networks with time-varying delays based on a fuzzy method. International Journal of Fuzzy Systems, 24(5):2203-2214, 2022.
 [12] Selvaraj P., Kwon O.M., Lee S.H., Sakthivel R. Cluster synchronization of fractional-order complex networks via uncertainty and disturbance estimator-based modified repetitive control. Journal of the Franklin Institute, 358(18):9951-9974, 2021.

@@ Line 28: / Line 28: @@
 In a similar vein, Ma et al. [8] ventured into the realm of topology identification for fractional-order complex networks, employing a strategy of variable substitution control. By devising a response network predicated on this control mechanism and a concurrent parameter update law, they derived a set of criteria for achieving both topology identification and network synchronization, with numerical simulations serving as a testament to the method’s validity. Collectively, these scholarly endeavors within the domains of switching topology and fractional-order complex networks not only enrich theoretical discourse but also chart a definitive course for empirical inquiry.
-In the realm of global research on switching topology and fractional-order complex networks, Ding et al. [9] have probed the intricacies of complex modified projective synchronization (CMPS) and the parameter estimation within time-varying coupled fractional-order complex-valued dynamic networks (FOCDN). Their theoretical discourse posits that FOCDN, when faced with time-varying delays, can attain CMPS via adaptive controllers—a premise substantiated by two numerical exemplars within the complex-valued domain, thereby affirming the potency of the refined projection strategy for fractional-order complex networks. Concurrently, Feifei et al. [10] have delved into the delay-dependent finite-time synchronization (FTS) criterion pertinent to a subset of fractional-order delay complex networks (FODCNs). By leveraging the Young inequality and the rules governing fractional-order derivatives of composite functions, they unveiled a novel delay-dependent fractional-order finite-time convergence principle (FOFTCP), wherein the stability duration is contingent upon the temporal delay. This newly minted FOFTCP, in concert with a meticulously crafted feedback controller, has yielded a fresh FTS criterion for FODCNs, the efficacy of which has been corroborated through two numerical demonstrations. In a parallel vein, Behinfaraz Reza et al. [11] have embarked on an exploration of the identification and synchronization within fractional-order complex networks, characterized by switching topology and time-variant delays, through the lens of fuzzy methodologies. The dynamics of the network nodes, deemed chaotic, were instantiated via a circuit realization tailored to these time-delay fractional-order dynamics. Employing T-S fuzzy modeling, they introduced an innovative representational paradigm for fractional-order chaotic systems, with simulations and empirical outcomes underscoring the proposed method's performance. Selvaraj  et al. [12] scrutinized the cluster synchronization and the mitigation of disturbances within fractional-order complex networks, beset by coupling delays, unknown uncertainties, and disturbances (UDs). A modified repetitive control (MRC) block was seamlessly integrated into a closed-loop feedback control circuit to tackle these challenges. Furthermore, they formulated a comprehensive suite of sufficient linear matrix inequality constraints to guarantee the system's cluster synchronization. The merits, practicability, and resilience of the MRC framework, predicated on UDE, were validated through two illustrative cases. This overview elucidates that international research endeavors in switching topology and fractional-order complex networks are markedly more focused than their domestic counterparts, thereby serving as a repository of valuable insights and benchmarks for domestic scholarly pursuits in these spheres.
+In the realm of global research on switching topology and fractional-order complex networks, Ding et al. [9] have probed the intricacies of complex modified projective synchronization (CMPS) and the parameter estimation within time-varying coupled fractional-order complex-valued dynamic networks (FOCDN). Their theoretical discourse posits that FOCDN, when faced with time-varying delays, can attain CMPS via adaptive controllers—a premise substantiated by two numerical exemplars within the complex-valued domain, thereby affirming the potency of the refined projection strategy for fractional-order complex networks. Concurrently, Du et al. [10] have delved into the delay-dependent finite-time synchronization (FTS) criterion pertinent to a subset of fractional-order delay complex networks (FODCNs). By leveraging the Young inequality and the rules governing fractional-order derivatives of composite functions, they unveiled a novel delay-dependent fractional-order finite-time convergence principle (FOFTCP), wherein the stability duration is contingent upon the temporal delay. This newly minted FOFTCP, in concert with a meticulously crafted feedback controller, has yielded a fresh FTS criterion for FODCNs, the efficacy of which has been corroborated through two numerical demonstrations. In a parallel vein, Behinfaraz Behinfaraz and Ghaemi [11] have embarked on an exploration of the identification and synchronization within fractional-order complex networks, characterized by switching topology and time-variant delays, through the lens of fuzzy methodologies. The dynamics of the network nodes, deemed chaotic, were instantiated via a circuit realization tailored to these time-delay fractional-order dynamics. Employing T-S fuzzy modeling, they introduced an innovative representational paradigm for fractional-order chaotic systems, with simulations and empirical outcomes underscoring the proposed method's performance. Selvaraj  et al. [12] scrutinized the cluster synchronization and the mitigation of disturbances within fractional-order complex networks, beset by coupling delays, unknown uncertainties, and disturbances (UDs). A modified repetitive control (MRC) block was seamlessly integrated into a closed-loop feedback control circuit to tackle these challenges. Furthermore, they formulated a comprehensive suite of sufficient linear matrix inequality constraints to guarantee the system's cluster synchronization. The merits, practicability, and resilience of the MRC framework, predicated on UDE, were validated through two illustrative cases. This overview elucidates that international research endeavors in switching topology and fractional-order complex networks are markedly more focused than their domestic counterparts, thereby serving as a repository of valuable insights and benchmarks for domestic scholarly pursuits in these spheres.
 ==2. Research content==

@@ Line 395: / Line 395: @@
 According to [[#img-6|Figure 6]], the network in Eq. (14), under the influence of the controller, can achieve synchronization. This numerical verification thus proves the validity of the three assumptions made in the model design.
-=4. Conclusion=
+==4. Conclusions==
 This scholarly endeavor commences with a meticulous literature review, canvassing both domestic and international sources to scaffold the theoretical underpinnings and discern the contemporary landscape of research in fractional-order complex networks. The exposition progresses to delineate the employed research methodologies, models, and controller architectures, thereby accentuating the pivotal themes under investigation. Culminating in a synthesis and discourse of the findings, the study arrives at several salient conclusions:
@@ Line 409: / Line 409: @@
 (5) Notwithstanding, the study acknowledges its constraints, notably the simplicity of the numerical simulations and the absence of an exhaustive dialogue. Future research trajectories will encompass a spectrum of simulation scenarios, varying parameters to dissect the outcomes under diverse conditions, thus rendering the conclusions more holistic and robust.
-==References:==
+==References==
-[1] Wei Zhiqiang, Weng Zheming, Hua Yongchao, et al. Formation-Encirclement Tracking Control of Heterogeneous Unmanned Clusters under Switching Topology. Journal of Aeronautics, 2023, 44(2): 252-267.
+[1] Wei Z., Weng Z., Hua Y., et al. Formation-encirclement tracking control of heterogeneous unmanned clusters under switching topology. Journal of Aeronautics, 44(2):252-267, 2023.
-[2] Chen Yinjuan, Ning Xiaogang, Wei Yongdong, et al. Consistency Iterative Learning Control of Measurement Restricted Multi-agent Systems under Switching Topology. Control Theory and Applications, 2023, 40(8): 1384-1394.
+[2] Chen Y., Ning X., Wei Y., et al. Consistency iterative learning control of measurement restricted multi-agent systems under switching topology. Control Theory and Applications, 40(8):1384-1394, 2023.
-[3] Huang Rujia, Jiang Nan, Liu Xiaoyang, et al. Bipartite Synchronization of Coupled Complex-valued Neural Networks under Switching Topology. Journal of Jiangsu Normal University (Natural Science Edition), 2023, 41(2): 51-58.
+[3] Huang R., Jiang N., Liu X., et al. Bipartite synchronization of coupled complex-valued neural networks under switching topology. Journal of Jiangsu Normal University (Natural Science Edition), 41(2):51-58, 2023.
-[4] Wang Qingling, Wang Xuerao. Adaptive Neural Network Consistency of Nonlinear Multi-agent Systems under Switching Topology. Control Theory and Applications, 2023, 40(4): 633-640.
+[4] Wang Q., Wang X. Adaptive neural network consistency of nonlinear multi-agent systems under switching topology. Control Theory and Applications, 40(4):633-640, 2023.
-[5] Meng Xiaoling, Mao Beixing. Two Methods of Sliding Mode Synchronization for Fractional-order Uncertain Complex Network Systems. Journal of Anhui University (Natural Science Edition), 2021, 45(6): 13-18.
+[5] Meng X., Mao B. Two methods of sliding mode synchronization for fractional-order uncertain complex network systems. Journal of Anhui University (Natural Science Edition), 45(6):13-18, 2021.
-[6] Meng Xiaoling. Adaptive Proportional-Integral Sliding Mode Synchronization of Fractional-order Uncertain Complex Network Systems. Journal of Zhengzhou Institute of Aeronautical Industry Management, 2022, 40(6): 102-104, 109.
+[6] Meng X. Adaptive proportional-integral sliding mode synchronization of fractional-order uncertain complex network systems. Journal of Zhengzhou Institute of Aeronautical Industry Management, 40(6):102-104, 2022.
-[7] Yang Xin, Zhang Guangjun, Li Xueren, et al. Delayed Projection Synchronization and Parameter Identification of Two Fractional-order Complex Networks with Coupling Delays. Control and Decision, 2022, 37(6): 1479-1488.
+[7] Yang X., Zhang G., Li X., et al. Delayed projection synchronization and parameter identification of two fractional-order complex networks with coupling delays. Control and Decision, 37(6):1479-1488, 2022.
-[8] Ma Weiyuan, Li Zhiming, Dai Changping. Topology Identification of Fractional-order Complex Networks Based on Variable Substitution Control. Journal of Shandong University (Science Edition), 2023, 58(11): 53-60.
+[8] Ma W., Li Z., Dai C. Topology identification of fractional-order complex networks based on variable substitution control. Journal of Shandong University (Science Edition), 58(11):53-60, 2023.
-[9]Ding D,Jiang Q,Hu Y,et al.Complex modified projective synchronization of fractional-order complex-valued dynamic network with time-varying coupling and parameters estimation.International Journal of Modern Physics C,2023,34(07).
+[9] Ding D., Jiang Q., Hu Y., et al. Complex modified projective synchronization of fractional-order complex-valued dynamic network with time-varying coupling and parameters estimation. International Journal of Modern Physics C, 34(07), 2350084, 2023.
-[10]Feifei D,Jun-Guo L,Qing-Hao Z.Delay-dependent finite-time synchronization criterion of fractional-order delayed complex networks.Communications in Nonlinear Science and Numerical Simulation,2023,119.
+[10] Du F., Lu J.G., Zhang Q.H.. Delay-dependent finite-time synchronization criterion of fractional-order delayed complex networks. Communications in Nonlinear Science and Numerical Simulation, 119, 107072, 2023.
-[11]Reza B,Sehraneh G.Identification and Synchronization of Switching Fractional-Order Complex Networks with Time-Varying Delays Based on a Fuzzy Method.International Journal of Fuzzy Systems,2022,24(5):2203-2214.
+[11] Reza B., Sehraneh G. Identification and synchronization of switching fractional-order complex networks with time-varying delays based on a fuzzy method. International Journal of Fuzzy Systems, 24(5):2203-2214, 2022.
-[12]P.S,O.M.K,S.H.L,et al.Cluster synchronization of fractional-order complex networks via uncertainty and disturbance estimator-based modified repetitive control.Journal of the Franklin Institute,2021,358(18):9951-9974.
+[12] Selvaraj P., Kwon O.M., Lee S.H., Sakthivel R. Cluster synchronization of fractional-order complex networks via uncertainty and disturbance estimator-based modified repetitive control. Journal of the Franklin Institute, 358(18):9951-9974, 2021.

@@ Line 371: / Line 371: @@
 |}
-where <math display="inline">k  </math> is a natural number equal to 1, 2, 3. Assuming the switching moments are <math display="inline">t_k=1.5</math>k, the sequence of switching among the three communication topologies is represented as <math display="inline">1\to 2\to 3\to 2 \to 1\to...</math>. This shows that the joint connectivity adjustment between nodes is feasible within the assumptions of this section. Numerical verification is then conducted based on the initial conditions set in Eq. (14), as illustrated in [[#img-5|Figures 5]] and [[#img-6|6]].
+where <math display="inline">k  </math> is a natural number equal to <math display="inline">1,\, 2,\, 3</math>. Assuming the switching moments are <math display="inline">t_k=1.5</math>k, the sequence of switching among the three communication topologies is represented as <math display="inline">1\to 2\to 3\to 2 \to 1\to...</math>. This shows that the joint connectivity adjustment between nodes is feasible within the assumptions of this section. Numerical verification is then conducted based on the initial conditions set in Eq. (14), as illustrated in [[#img-5|Figures 5]] and [[#img-6|6]].
 <div id='img-5'></div>

← Older revision		Revision as of 10:35, 21 June 2024
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−	Here, <math display="inline"> n </math> is a natural number equal to 1, 2, 3. Assuming the switching moments are <math display="inline">t_k=k</math>, the sequence of switching among the three communication topology is represented as <math display="inline">1\to 2\to 3\to 1\to...</math>. Thus, it can be seen that in this section's assumption, the joint connectivity adjustment between nodes is feasible. Selecting the initial conditions from the model design, numerical verification can be performed as shown in [[#img-2\|Figures 2]] and [[#img-3\|3]].	+	Here, <math display="inline"> n </math> is a natural number equal to <math display="inline">1,\, 2,\, 3</math>. Assuming the switching moments are <math display="inline">t_k=k</math>, the sequence of switching among the three communication topology is represented as <math display="inline">1\to 2\to 3\to 1\to...</math>. Thus, it can be seen that in this section's assumption, the joint connectivity adjustment between nodes is feasible. Selecting the initial conditions from the model design, numerical verification can be performed as shown in [[#img-2\|Figures 2]] and [[#img-3\|3]].

	<div id='img-2'></div>		<div id='img-2'></div>

@@ Line 53: / Line 53: @@
 {| style="text-align: center; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math> a_{ij}^n \begin{cases}c_{ij},i\neq j\,\text{just}\, \left(\nu_i,\nu_j\right)\in\varepsilon^n\\ 0,\, \text{Other situations}\end{cases}  </math>
+| style="text-align: center;" | <math> a_{ij}^n \begin{cases}c_{ij},\quad i\neq j\,\text{just}\, \left(\nu_i,\nu_j\right)\in\varepsilon^n\\ 0,\quad \text{Other situations}\end{cases}  </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" |(1)

@@ Line 387: / Line 387: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:auto;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[File:6666.png|600744x744px]]
+|style="text-align: center;padding:10px;"| [[File:6666.png|600px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 6'''. Time course change of synchronization error under the influence of a controller