Group Consensus in Networked Gyroscopes Systems Using the Udwadia-Kalaba Fundamental Equation Theory
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- 英文论文题名：Group Consensus in Networked Gyroscopes Systems Using the Udwadia-Kalaba Fundamental Equation Theory
- 论文作者：Jun Liu ; Liyun Zhao
- 英文论文作者：Jun Liu ; Liyun Zhao ; Department of Mathematics ; Jining University ; School of Mathematics ; Physics and Biological Engineering ; Inner Mongolia University of Science and Technology
- 年：2017
- 作者机构：Department of Mathematics,Jining University;School of Mathematics,Physics and Biological Engineering,Inner Mongolia University of Science and Technology;
- 英文论文关键词：Group consensus ; Udwadia-Kalaba fundamental equation ; networked gyroscopes ; directed networks
- 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：O175
- 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：5
- 文件大小：341k
- 原文格式：D
- 会议级别：全国
摘要
This paper provides a simple approach for group consensus of networked gyroscopes systems from the analytical dynamics point of view. By using the Udwadia-Kalaba fundamental equation theory, a novel robust group control law is presented and a sufficient condition which ensure achieving group consensus of non-identical gyroscopes networks is given in this paper. Finally, numerical simulations conducted on networks composed by five non-identical gyroscopes is given to demonstrate effectiveness of the proposed control methodology.
This paper provides a simple approach for group consensus of networked gyroscopes systems from the analytical dynamics point of view. By using the Udwadia-Kalaba fundamental equation theory, a novel robust group control law is presented and a sufficient condition which ensure achieving group consensus of non-identical gyroscopes networks is given in this paper. Finally, numerical simulations conducted on networks composed by five non-identical gyroscopes is given to demonstrate effectiveness of the proposed control methodology.
This paper provides a simple approach for group consensus of networked gyroscopes systems from the analytical dynamics point of view. By using the Udwadia-Kalaba fundamental equation theory, a novel robust group control law is presented and a sufficient condition which ensure achieving group consensus of non-identical gyroscopes networks is given in this paper. Finally, numerical simulations conducted on networks composed by five non-identical gyroscopes is given to demonstrate effectiveness of the proposed control methodology.
引文
[1]Yu,J.and Wang,L.Group consensus in multi-agent systems with switching topologies and communication delays.Systems&Control Letters,2010,59(6):340-348.
[2]Liu,X,Chen,T.Cluster synchronization in directed networks via intermittent pinning control.IEEE Transactions on Neural Networks,2011,22(7):1009-1020.
[3]Chen Y,L J,Han F,et al.On the cluster consensus of discretetime multi-agent systems.Systems&Control Letters,2011,60(7):517-523.
[4]Su,H,Chen,M.Z.Q.,Wang,X,et al.Adaptive cluster synchronisation of coupled harmonic oscillators with multiple leaders.IET Control Theory&Applications,2013,7(5):765-772.
[5]Qin,J.and Yu,C.Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition.Automatica,2013,49(9):2898-2905.
[6]Yu,C,Qin,J.and Gao,H.Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control.Automatica,2014,50(9):2341-2349.
[7]Xia,W.and Cao,M.Clustering in diffusively coupled networks.Automatica,2011,47(11):2395-2405.
[8]Wu,W.,Zhou,W.,and Chen,T.Cluster synchronization of linearly coupled complex networks under pinning control.IEEE Transactions on Circuits and Systems I:Regular Papers,2009,56(4):829-839.
[9]Liu,J.and Zhou,J.Distributed impulsive group consensus in second-order multi-agent systems under directed topology.International Journal of Control,2015,88(5):910-919.
[10]Liu,J.,Ji,J.,Zhou,J.,et al.Adaptive group consensus in uncertain networked Euler CLagrange systems under directed topology.Nonlinear Dynamics,2015,82(3):1145-1157.
[11]Udwadia,F.E.and Kalaba,R.E.A new perspective on constrained motion.Proceedings of the Royal Society A,439,407–410(1992).
[12]Udwadia,F.E.and Kalaba,R.E.What is the general form of the explicit equations of motion for constrained mechanical systems.Journal of Dynamic Systems Measurement and Control-transactions of The ASME,69,335–339(2002).
[13]Udwadia,F.E.A new perspective on the tracking control of nonlinear structural and mechanical systems.Proceedings of the Royal Society A,459(2035),1783–1800(2003).
[14]Udwadia,F.E.and Han,B.Synchronization of multiple chaotic gyroscopes using the fundamental equation of mechanics.Journal of Applied Mechanics-transactions of the ASME,75(2),021011(2008).
[15]Udwadia,F.E.and Schutte,A.D.A unified approach to rigid body rotational dynamics and control.Proceedings of the Royal Society A,468(2138),395–414(2012).
[16]Schutte,A.D.and Udwadia,F.E.New approach to the modeling of complex multibody dynamical systems.Journal of Applied Mechanics-transactions of the ASME,78(2),021018(2011).
[17]Udwadia,F.E.,Optimal tracking control of nonlinear dynamical systems.Proceedings of the Royal Society A,464(2097),2341–2363(2008).
[18]Udwadia,F.E.and Schutte,A.D.An alternative derivation of the quaternion equations of motion for rigid-body rotational dynamics.Journal of Applied Mechanics-transactions of the ASME,77(4),044505(2010).
[19]Udwadia,F.E.and Kalaba,R.E.Analytical dynamics:a new approach.Cambridge University Press,Cambridge,(1996).
[20]Zhao H,Zhen S,Chen Y H.Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory.Chinese Journal of Mechanical Engineering,2013,26(5):839-850.
[21]Huang J,Chen Y H,Zhong Z.Udwadia-Kalaba Approach for Parallel Manipulator Dynamics.Journal of Dynamic Systems,Measurement,and Control-transactions of the ASME,2013,135(6):061003.
[22]Liu,J.,Ji,J.,and Zhou J.Synchronization of networked multibody systems using fundamental equation of mechanics.Applied Mathematics and Mechanics,2016,37(5):555-572.
[2]Liu,X,Chen,T.Cluster synchronization in directed networks via intermittent pinning control.IEEE Transactions on Neural Networks,2011,22(7):1009-1020.
[3]Chen Y,L J,Han F,et al.On the cluster consensus of discretetime multi-agent systems.Systems&Control Letters,2011,60(7):517-523.
[4]Su,H,Chen,M.Z.Q.,Wang,X,et al.Adaptive cluster synchronisation of coupled harmonic oscillators with multiple leaders.IET Control Theory&Applications,2013,7(5):765-772.
[5]Qin,J.and Yu,C.Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition.Automatica,2013,49(9):2898-2905.
[6]Yu,C,Qin,J.and Gao,H.Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control.Automatica,2014,50(9):2341-2349.
[7]Xia,W.and Cao,M.Clustering in diffusively coupled networks.Automatica,2011,47(11):2395-2405.
[8]Wu,W.,Zhou,W.,and Chen,T.Cluster synchronization of linearly coupled complex networks under pinning control.IEEE Transactions on Circuits and Systems I:Regular Papers,2009,56(4):829-839.
[9]Liu,J.and Zhou,J.Distributed impulsive group consensus in second-order multi-agent systems under directed topology.International Journal of Control,2015,88(5):910-919.
[10]Liu,J.,Ji,J.,Zhou,J.,et al.Adaptive group consensus in uncertain networked Euler CLagrange systems under directed topology.Nonlinear Dynamics,2015,82(3):1145-1157.
[11]Udwadia,F.E.and Kalaba,R.E.A new perspective on constrained motion.Proceedings of the Royal Society A,439,407–410(1992).
[12]Udwadia,F.E.and Kalaba,R.E.What is the general form of the explicit equations of motion for constrained mechanical systems.Journal of Dynamic Systems Measurement and Control-transactions of The ASME,69,335–339(2002).
[13]Udwadia,F.E.A new perspective on the tracking control of nonlinear structural and mechanical systems.Proceedings of the Royal Society A,459(2035),1783–1800(2003).
[14]Udwadia,F.E.and Han,B.Synchronization of multiple chaotic gyroscopes using the fundamental equation of mechanics.Journal of Applied Mechanics-transactions of the ASME,75(2),021011(2008).
[15]Udwadia,F.E.and Schutte,A.D.A unified approach to rigid body rotational dynamics and control.Proceedings of the Royal Society A,468(2138),395–414(2012).
[16]Schutte,A.D.and Udwadia,F.E.New approach to the modeling of complex multibody dynamical systems.Journal of Applied Mechanics-transactions of the ASME,78(2),021018(2011).
[17]Udwadia,F.E.,Optimal tracking control of nonlinear dynamical systems.Proceedings of the Royal Society A,464(2097),2341–2363(2008).
[18]Udwadia,F.E.and Schutte,A.D.An alternative derivation of the quaternion equations of motion for rigid-body rotational dynamics.Journal of Applied Mechanics-transactions of the ASME,77(4),044505(2010).
[19]Udwadia,F.E.and Kalaba,R.E.Analytical dynamics:a new approach.Cambridge University Press,Cambridge,(1996).
[20]Zhao H,Zhen S,Chen Y H.Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory.Chinese Journal of Mechanical Engineering,2013,26(5):839-850.
[21]Huang J,Chen Y H,Zhong Z.Udwadia-Kalaba Approach for Parallel Manipulator Dynamics.Journal of Dynamic Systems,Measurement,and Control-transactions of the ASME,2013,135(6):061003.
[22]Liu,J.,Ji,J.,and Zhou J.Synchronization of networked multibody systems using fundamental equation of mechanics.Applied Mathematics and Mechanics,2016,37(5):555-572.