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Asymptotic stability for non-cooperative program game model of the capacity analysis for mobile ad-hoc networks with variable time delay

Yang Juan Yang Dan Huang Bin Zhang Xiao-Hong Yang Cong

Asymptotic stability for non-cooperative program game model of the capacity analysis for mobile ad-hoc networks with variable time delay

Yang Juan, Yang Dan, Huang Bin, Zhang Xiao-Hong, Yang Cong
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  • Stability of capacity is one of the key properties for quality of service (QoS) support in mobile ad hoc networks (MANETs). In this paper, a novel technique is proposed for controlling the stability of capacity analysis model for non-cooperative program game MANETs, with the time-varying propagation delay taken into consideration. First, based on the obtained source node flow transmitting rate evolution aligns of capacity analysis model for non-cooperative program game mobile ad-hoc network, when adding the time-varying propagation delay term, which is a class of nonlinear time-varying delay differential aligns, the asymptotic stability criteria of the model are presented in the form of descriptor and linear matrix inequalities. Then, an iterative algorithm is also provided for controlling the stability of the model. The proposed criteria are less conservative since they are based on an equivalent model transformation. Simulation experiments verify the effectiveness of this algorithm. Although the model used in this paper focuses on a specific algorithm, we believe that this method has a great potential in analyzing and understanding the general capacity of MANETs stability control issues.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61173131), Central Universities Fundamental Research Interdisciplinary Class Major Projects, China (Grant No. CDJZR12098801), Based and Advanced Research Projects of Chongqing of China (Grant No. cstc2013jcyjA40033), Key Strategic Project of Chongqing of China (Grant No. CSTC2009AB2230), Strategeic Project of Chongqing of China (Grant No. 2009AC2057), and the Special funding for Scientific Research Project of Chongqing Postdoctoral Researchers, China (Grant No. XM20120054).
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    [2]

    Grossglauser M, Tse D N C 2002 IEEE/ACM Trans. Networ. 10 477

    [3]

    Zhao S M, Liu J 2010 Acta Phys. Sin. 59 771 (in Chinese) [赵生妹, 刘静 2010 物理学报 59 771]

    [4]

    Shirong D, John N D, Bahram A 2011 Ad-Hoc Net. 9 120

    [5]

    Zhao H T, Emiliano G P, Jibo W, Yong X 2011 Phys. Comun. 4 98

    [6]

    Zhong L, Wang C, Jiang C J, Li X Y 2013 Ad-Hoc Net. 11 29

    [7]

    Wang L J, Cai L, Liu X Z 2009 Comput. Net. 53 338

    [8]

    Tassiulas L 1997 IEEE Trans. Inform. Theory 43 106

    [9]

    Li W X, Su H, Wang K 2011 Automatica 47 215

    [10]

    Feijer D, Paganini F 2010 Automatica. 46 1974

    [11]

    Dargie W, Schill A 2011 J. Comput. Syst. Sci. 77 852

    [12]

    Chen C H, Yin C C, Yue G X 2011 J. China Universities of Posts and Telecommunications 18 22

    [13]

    Jae Y S, Seong L K 2012 Comput. Commun. 35 1345

    [14]

    Kherani A, El-Khoury R, El-Azouzi R 2008 Comput. Net. 52 1365

    [15]

    Liu S, Liu B, Zhang Y K, Wen Y 2010 Acta Phys. Sin. 59 38 (in Chinese) [刘爽, 刘彬, 张业宽, 闻岩 2010 物理学报 59 38]

    [16]

    Shi P M, Li J Z, Liu B, Han D Y 2011 Acta Phys. Sin. 60 94501 (in Chinese) [时培明, 李纪召, 刘彬, 韩东颖 2011 物理学报 60 094501]

    [17]

    Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明, 刘彬, 侯东晓 2008 物理学报 57 1321]

    [18]

    Kherani A, El-Khoury R, El-Azouzi R 2008 Comput. Networks. 52 1365

    [19]

    Yamamoto K, 2005 IEICE T. Commun. E88-B 1009

    [20]

    Farhadi A, 2010 Charalambousb D: Automatica 46 889

    [21]

    Yang J, Li Y, Zhang Z J, Li J Q 2012 JEIT 34 75 (in Chinese) [杨娟, 李颖, 张志军, 李季青 2012 电子与信息学报 34 75]

    [22]

    Li C D, Liao X F 2006 Int. J. Bifurcat. Chaos 16 3323

    [23]

    Liao X F, Li C D 2007 Int. J. Bifurcat. Chaos 18 342

    [24]

    Arik S 2002 IEEE Trans. Neural Networks 13 1239

    [25]

    Cao J D 2001 IEEE Trans. CAS I 48 1330

    [26]

    Hale J, Verduyn Lunel SM 1993 Introduction to Functional Differential Aligns (New York: Springer) p332

    [27]

    Kolmanovskii V, Nosov V 1986 Stability of Functional Differential Aligns (New York: Academic Press) p214

    [28]

    Zhang H G, Wang Z L, Wang Z S 2006 Acta Phys. Sin. 55 2687 (in Chinese) [张化光, 王智良, 王占山 2006 物理学报 55 2687]

    [29]

    Gopalsamy K 1992 Ph. D. Dissertation (The Netherlands: Kluwer Academic)

    [30]

    Liao X F, Liu Y B, Guo S T, Huanhuan M 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3120

    [31]

    Fridman E 2001 Syst. Control Lett. 43 309

    [32]

    Yang J 2011 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [杨娟 2011博士学位论文 (重庆: 重庆大学)]

    [33]

    Liao X X 2002 Theory Methods and Application of Stability (Wuhan: Press of Huazhong University of Science and Technology) p40 (in Chinese) [廖晓昕 2002 稳定性的理论、方法和应用 (武汉: 华中科技大学 出版社) 第40页]

    [34]

    Kolamnovskii V, Myshkis A 1999 Applied Theory of Functional Differential Aligns (Boston (MA): Kluwer) p59

    [35]

    Alpcan T, Basar T 2005 IEEE/ACM Trans. Networ. 13 1261

    [36]

    Wu M, He Y 2008 Delay System Robust Control-Liberty Matrix Method (Beijing: Science Press) p1 (in Chinese) [吴敏, 何勇 2008 时滞系统鲁棒控制——自由权矩阵方法 (北京: 科学出版社) 第1页]

  • [1]

    Gupta P, Kumar P 2000 IEEE Trans. Inform. Theory 46 388

    [2]

    Grossglauser M, Tse D N C 2002 IEEE/ACM Trans. Networ. 10 477

    [3]

    Zhao S M, Liu J 2010 Acta Phys. Sin. 59 771 (in Chinese) [赵生妹, 刘静 2010 物理学报 59 771]

    [4]

    Shirong D, John N D, Bahram A 2011 Ad-Hoc Net. 9 120

    [5]

    Zhao H T, Emiliano G P, Jibo W, Yong X 2011 Phys. Comun. 4 98

    [6]

    Zhong L, Wang C, Jiang C J, Li X Y 2013 Ad-Hoc Net. 11 29

    [7]

    Wang L J, Cai L, Liu X Z 2009 Comput. Net. 53 338

    [8]

    Tassiulas L 1997 IEEE Trans. Inform. Theory 43 106

    [9]

    Li W X, Su H, Wang K 2011 Automatica 47 215

    [10]

    Feijer D, Paganini F 2010 Automatica. 46 1974

    [11]

    Dargie W, Schill A 2011 J. Comput. Syst. Sci. 77 852

    [12]

    Chen C H, Yin C C, Yue G X 2011 J. China Universities of Posts and Telecommunications 18 22

    [13]

    Jae Y S, Seong L K 2012 Comput. Commun. 35 1345

    [14]

    Kherani A, El-Khoury R, El-Azouzi R 2008 Comput. Net. 52 1365

    [15]

    Liu S, Liu B, Zhang Y K, Wen Y 2010 Acta Phys. Sin. 59 38 (in Chinese) [刘爽, 刘彬, 张业宽, 闻岩 2010 物理学报 59 38]

    [16]

    Shi P M, Li J Z, Liu B, Han D Y 2011 Acta Phys. Sin. 60 94501 (in Chinese) [时培明, 李纪召, 刘彬, 韩东颖 2011 物理学报 60 094501]

    [17]

    Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明, 刘彬, 侯东晓 2008 物理学报 57 1321]

    [18]

    Kherani A, El-Khoury R, El-Azouzi R 2008 Comput. Networks. 52 1365

    [19]

    Yamamoto K, 2005 IEICE T. Commun. E88-B 1009

    [20]

    Farhadi A, 2010 Charalambousb D: Automatica 46 889

    [21]

    Yang J, Li Y, Zhang Z J, Li J Q 2012 JEIT 34 75 (in Chinese) [杨娟, 李颖, 张志军, 李季青 2012 电子与信息学报 34 75]

    [22]

    Li C D, Liao X F 2006 Int. J. Bifurcat. Chaos 16 3323

    [23]

    Liao X F, Li C D 2007 Int. J. Bifurcat. Chaos 18 342

    [24]

    Arik S 2002 IEEE Trans. Neural Networks 13 1239

    [25]

    Cao J D 2001 IEEE Trans. CAS I 48 1330

    [26]

    Hale J, Verduyn Lunel SM 1993 Introduction to Functional Differential Aligns (New York: Springer) p332

    [27]

    Kolmanovskii V, Nosov V 1986 Stability of Functional Differential Aligns (New York: Academic Press) p214

    [28]

    Zhang H G, Wang Z L, Wang Z S 2006 Acta Phys. Sin. 55 2687 (in Chinese) [张化光, 王智良, 王占山 2006 物理学报 55 2687]

    [29]

    Gopalsamy K 1992 Ph. D. Dissertation (The Netherlands: Kluwer Academic)

    [30]

    Liao X F, Liu Y B, Guo S T, Huanhuan M 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 3120

    [31]

    Fridman E 2001 Syst. Control Lett. 43 309

    [32]

    Yang J 2011 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [杨娟 2011博士学位论文 (重庆: 重庆大学)]

    [33]

    Liao X X 2002 Theory Methods and Application of Stability (Wuhan: Press of Huazhong University of Science and Technology) p40 (in Chinese) [廖晓昕 2002 稳定性的理论、方法和应用 (武汉: 华中科技大学 出版社) 第40页]

    [34]

    Kolamnovskii V, Myshkis A 1999 Applied Theory of Functional Differential Aligns (Boston (MA): Kluwer) p59

    [35]

    Alpcan T, Basar T 2005 IEEE/ACM Trans. Networ. 13 1261

    [36]

    Wu M, He Y 2008 Delay System Robust Control-Liberty Matrix Method (Beijing: Science Press) p1 (in Chinese) [吴敏, 何勇 2008 时滞系统鲁棒控制——自由权矩阵方法 (北京: 科学出版社) 第1页]

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Publishing process
  • Received Date:  12 August 2013
  • Accepted Date:  28 October 2013
  • Published Online:  20 January 2014

Asymptotic stability for non-cooperative program game model of the capacity analysis for mobile ad-hoc networks with variable time delay

  • 1. College of Communication Engineering, Chongqing University, Chongqing 400030, China;
  • 2. The 3rd Department, PLA.Chongqing Communication Institute, Chongqing 400035, China;
  • 3. School of Software Engineering, Chongqing University, Chongqing 400030, China;
  • 4. Foundation department, PLA.Chongqing Communication College, Chongqing 400035, China;
  • 5. The1rd Department, PLA.Chongqing Communication Institute, Chongqing 400035, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 61173131), Central Universities Fundamental Research Interdisciplinary Class Major Projects, China (Grant No. CDJZR12098801), Based and Advanced Research Projects of Chongqing of China (Grant No. cstc2013jcyjA40033), Key Strategic Project of Chongqing of China (Grant No. CSTC2009AB2230), Strategeic Project of Chongqing of China (Grant No. 2009AC2057), and the Special funding for Scientific Research Project of Chongqing Postdoctoral Researchers, China (Grant No. XM20120054).

Abstract: Stability of capacity is one of the key properties for quality of service (QoS) support in mobile ad hoc networks (MANETs). In this paper, a novel technique is proposed for controlling the stability of capacity analysis model for non-cooperative program game MANETs, with the time-varying propagation delay taken into consideration. First, based on the obtained source node flow transmitting rate evolution aligns of capacity analysis model for non-cooperative program game mobile ad-hoc network, when adding the time-varying propagation delay term, which is a class of nonlinear time-varying delay differential aligns, the asymptotic stability criteria of the model are presented in the form of descriptor and linear matrix inequalities. Then, an iterative algorithm is also provided for controlling the stability of the model. The proposed criteria are less conservative since they are based on an equivalent model transformation. Simulation experiments verify the effectiveness of this algorithm. Although the model used in this paper focuses on a specific algorithm, we believe that this method has a great potential in analyzing and understanding the general capacity of MANETs stability control issues.

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