The Orientation Control Of The Tree-Shaped Strings Network
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- 英文论文题名：The Orientation Control Of The Tree-Shaped Strings Network
- 论文作者：Yaru Xie ; Genqi Xu
- 英文论文作者：Yaru Xie ; Genqi Xu ; Department of Mathematics ; Tianjin University
- 年：2017
- 作者机构：Department of Mathematics,Tianjin University;
- 英文论文关键词：Orientation control ; Anti-disturbance ; Convergence of network ; Lyapunov method
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：214k
- 原文格式：D
- 会议级别：全国
摘要
In the present paper, we study the orientation control of tree-shaped strings network by the approach feedforward control. First, we design a new controller through the dynamics condition of objective network to stabilize the boundary node a1,a2, a3 and have no effect the other part of network. Furthermore, the convergence of network system continue to be discussed under some control strategy when one of the dynamics condition of the boundary w_(3,x)(1, t) is unknown and the original network is still proved to converge to the network of target structure. The method here is appropriate for more complex graph and mathematical model.
In the present paper, we study the orientation control of tree-shaped strings network by the approach feedforward control. First, we design a new controller through the dynamics condition of objective network to stabilize the boundary node a1,a2, a3 and have no effect the other part of network. Furthermore, the convergence of network system continue to be discussed under some control strategy when one of the dynamics condition of the boundary w_(3,x)(1, t) is unknown and the original network is still proved to converge to the network of target structure. The method here is appropriate for more complex graph and mathematical model.
In the present paper, we study the orientation control of tree-shaped strings network by the approach feedforward control. First, we design a new controller through the dynamics condition of objective network to stabilize the boundary node a1,a2, a3 and have no effect the other part of network. Furthermore, the convergence of network system continue to be discussed under some control strategy when one of the dynamics condition of the boundary w_(3,x)(1, t) is unknown and the original network is still proved to converge to the network of target structure. The method here is appropriate for more complex graph and mathematical model.
引文
[1]K.Ammari and M.Jellouli,Stabilization of star-shaped tree of elastic strings,Diferential and Integral Equation,17(11-12):1395–1410,2004.
[2]S.Nicaise and J.Valein,Stablization of the wave equation on 1-d networks with a delay term in the nodal feedbacks,Networks and Heterogeneous Media,2007.
[3]J.Valein and E.Zuazua,Stabilization of the wave equation on 1-d networks,SIAM Journal on control and Optimization,48(4):2771–2797,2009.
[4]G.Q.Xu,D.Y.Liu,Y.Q.Liu,Abstract second order hyperbolic system and applications to controlled network of strings,SIAM J.Control Opthim,47,2008.
[5]G.Q.Xu and N.E.Mastorakis,Differential Equation on Metric Graph,WSEAS publisher,Athens,2010.
[6]K.S.Liu,F.L.Huang and G.Chen,Exponential stability analysis of a long chain of coupled vibrating strings with dissipative linkage,Siam Journal on Applied Mathematics,49:1694–1707,1989.
[7]E.Schmidt,On the modelling and exact controllability of networks of vibrating strings,Siam Journal on Control&Optimization,30:229–245,1992.
[8]J.E.Lagnese,G.Leugering and E.Schmidt,Modelling,Analysis and Control of Dynamic Elastic Multi-Link Structures,Systems&Control:Foundations&Applications,1994.
[9]J.E.Lagnese,Recent progress and open problems in control of multi-link elastic structures,Contemp.Math,209:161–175,1997.
[10]G.Leugering and E.Zuazua,On exact controllability of generic trees,Esaim Proceedings,8:95–105,2000.
[11]G.Leugering,Dynamic domain decomposition of optimal control problems for networks of strings and Timoshenko beams,SIAM Journal on Control&Optimization,37:1649–1675,1999.
[12]R.Dager and E.Zuazua,Controllability of star-shaped networks of strings,C.R.Acad.Sci.Paris,Series I,332:621–626,2001.
[13]R.Dager,Observation and control of vibrations in treeshaped networks of strings,SIAM J.Control&Optim,43:590–623,2004.
[14]R.Dager and E.Zuazua,Wave Propagation,Observation and Control in 1-d Flexible Multi-Structures,Springer Berlin,2006.
[15]K.Ammari and M.Jellouli,Stabilization of star-shaped tree of elastic strings,Differential&Integral Equations,17:1395–1410,2004.
[16]K.Ammari,M.Jellouli and M.Khenissi,Stabilization of generic trees of strings,Journal of Dynamical&Control Systems,11:177–193,2005.
[2]S.Nicaise and J.Valein,Stablization of the wave equation on 1-d networks with a delay term in the nodal feedbacks,Networks and Heterogeneous Media,2007.
[3]J.Valein and E.Zuazua,Stabilization of the wave equation on 1-d networks,SIAM Journal on control and Optimization,48(4):2771–2797,2009.
[4]G.Q.Xu,D.Y.Liu,Y.Q.Liu,Abstract second order hyperbolic system and applications to controlled network of strings,SIAM J.Control Opthim,47,2008.
[5]G.Q.Xu and N.E.Mastorakis,Differential Equation on Metric Graph,WSEAS publisher,Athens,2010.
[6]K.S.Liu,F.L.Huang and G.Chen,Exponential stability analysis of a long chain of coupled vibrating strings with dissipative linkage,Siam Journal on Applied Mathematics,49:1694–1707,1989.
[7]E.Schmidt,On the modelling and exact controllability of networks of vibrating strings,Siam Journal on Control&Optimization,30:229–245,1992.
[8]J.E.Lagnese,G.Leugering and E.Schmidt,Modelling,Analysis and Control of Dynamic Elastic Multi-Link Structures,Systems&Control:Foundations&Applications,1994.
[9]J.E.Lagnese,Recent progress and open problems in control of multi-link elastic structures,Contemp.Math,209:161–175,1997.
[10]G.Leugering and E.Zuazua,On exact controllability of generic trees,Esaim Proceedings,8:95–105,2000.
[11]G.Leugering,Dynamic domain decomposition of optimal control problems for networks of strings and Timoshenko beams,SIAM Journal on Control&Optimization,37:1649–1675,1999.
[12]R.Dager and E.Zuazua,Controllability of star-shaped networks of strings,C.R.Acad.Sci.Paris,Series I,332:621–626,2001.
[13]R.Dager,Observation and control of vibrations in treeshaped networks of strings,SIAM J.Control&Optim,43:590–623,2004.
[14]R.Dager and E.Zuazua,Wave Propagation,Observation and Control in 1-d Flexible Multi-Structures,Springer Berlin,2006.
[15]K.Ammari and M.Jellouli,Stabilization of star-shaped tree of elastic strings,Differential&Integral Equations,17:1395–1410,2004.
[16]K.Ammari,M.Jellouli and M.Khenissi,Stabilization of generic trees of strings,Journal of Dynamical&Control Systems,11:177–193,2005.