移动多智能体网络的分散式Markov跳变路由控制策略
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摘要
本文的主要目的就是讨论转移概率己知和部分已知时多智能体系统的稳定性问题及马尔科夫跳变路由控制策略,具体内容为：首先我们给出了在多智能体系统下的随机稳定性的定义。基于这个定义,我们针对连续时间马尔科夫跳变系统,通过合理的选取Lyapunov函数,得到了系统在转移概率完全己知情况下的稳定性分析结果。紧接着,在分析结果的基础上,我们给出了使系统稳定的控制器设计方法。其次针对实际应用中大量出现的系统转移概率部分未知的情况,通过对系统转移概率的分析,我们得出了该条件下的系统稳定性分析结果。其方法同样是通过选取合理的Lyapunov函数。最后针对以上两种情况给出总结,并指出以后需要继续进行的工作和研究。需要说明的是,本文结论的计算结果完全基于线性矩阵不等式。
The main purpose of this paper is to discuss the stability problem and the Markov transition probability is completely known when the multi-agent system jump routing con-trol strategy, the specific contents are as follows:First, we give the definitions of stochastic stability in markov jump linear systems[15]. Based on this definition, we consider contin-uous time Markov jump systems, through the reasonable selection of Lyapunov function, the stability analysis result in the transition probability is completely known case. Then, based on the analysis of the results, we give the design method of the controller system stability. Secondly, the emergence of a large number of practical application system of partly unknown transition probabilities, by analyzing the probability of system transfer, we conclude that the stability of the system under the condition of the analysis results. The same method is to select the reasonable Lyapunov function.Finally, for the above two situations are summarized, and pointed out the need to continue the work and research. It is the conclusion of this paper, calculation results based on linear matrix inequality.
The main purpose of this paper is to discuss the stability problem and the Markov transition probability is completely known when the multi-agent system jump routing con-trol strategy, the specific contents are as follows:First, we give the definitions of stochastic stability in markov jump linear systems[15]. Based on this definition, we consider contin-uous time Markov jump systems, through the reasonable selection of Lyapunov function, the stability analysis result in the transition probability is completely known case. Then, based on the analysis of the results, we give the design method of the controller system stability. Secondly, the emergence of a large number of practical application system of partly unknown transition probabilities, by analyzing the probability of system transfer, we conclude that the stability of the system under the condition of the analysis results. The same method is to select the reasonable Lyapunov function.Finally, for the above two situations are summarized, and pointed out the need to continue the work and research. It is the conclusion of this paper, calculation results based on linear matrix inequality.
引文
[1]F. Abdollahi and K. Khorasani, "A decentralized Markovian jump H∞ control routing strategy for mobile multi-agent networked systems." IEEE Transactions on Control Systems Technology, vol.19, no.2, pp.269-283,2011.
[2]F. Abdollahi and K. Khorasani, "A novel H∞ control strategy for design of a robust dynamic routing algorithm in traffic networks," IEEE Journal on Selected Areas in Communications, vol.26, no.4, pp.706-718,2008.
[3]Xueming Si, Xun-Lin Zhu, Xin Du, and Xiangpeng Xie, "A decentralized routing control scheme for data communication networks." Mathematical Problems in Engi-neering.
[4]N. Chen, X. Zhang, and W. Gui, "Robust decentralized H∞ control of multi-channel uncertain time-delay systems:An LMI approach." Proceedings of IEEE International Conference on Mechatronics and Automation, pp.367-372,2006.
[5]Kokmae H, Kobayashi H, Mori T. "Robust Performance for Linear Delay-differential Systems with Time-varying Uncertainties [J]." IEEE AC(S0018-9286).1998,43(7):971-974
[6]杨柳,多智能体分布式协调控制,硕士学位论文,中山大学,2009.
[7]孙凤兰,多智能体网络的一致性研究,博士学位论文,华中科技大学,2012.
[8]吴正平.复杂网络建模与一致性及在多移动智能体中的应用：[PhD Dissertation].华中科技大学,2007.
[9]汪小帆,李翔,陈关荣.复杂网络理论及其应用.清华大学出版社,2006.
[10]刘智伟.基于混杂控制的复杂多智能体网络同步一致性研究：[PhD Dissertation].华中科技大学,2011.
[11]K. Gu, "An integral inequality in the stability problem of time-delay systems." Pro-ceedings of 39th IEEE Conference on Decision and Control,2000, pp.2805-2810.
[12]X. Zhu and Y. Wang, "Parameter-dependent switching law for linear switched sys-tems with time-varying delay." Proceedings of 9th IEEE International Con-ference on Control and Automation, pp.300-305,2011.
[13]Mahmoud M S, Shi P. "Methodologies for Control of Jump Time-Delay Systems[M]." Kluwer Academic Publishers.2003.
[14]Xue F, Kumar P. The number of neighbors needed for connectivity of wireless net-works.Wireless networks,2004,10(2):169-181.
[15]Mao X. "Stochastic Differential Equations and Their Applications[M]."Chichester. Honvood,1997.
[16]Boukas E. "Hoo control of discrete-time Markov jump systems with bounded transi-tion probabilities[J]. "Optimal Control Applications and Methods,2009,30(5):477-494.
[17]Fang Y G Loparo K A. "Stabilization of continuous time jump linear systems[J]." IEEE Transactions on Automatic Control,2002,47(10):1590.1630.
[18]Boukas E K,Shi P,Nguang S K. "Robust H∞ control for linear markov jump systems with unknow nonlinearties[J]." Journal of Mathematical Analysis and Applications, 2003,282(1):241-255.
[19]Krasovskii N N,Lidskii E A. "Analytical design of controllers in systems with random arributes[J]." Automation and Remote Control,1961,22:1021-1025.
[20]Jadbabaie A, Lin J, Morse A. Coordination of groups of mobile autonomous agents us-ing nearest neighbor rules. IEEE Transactions on Automatic Control,2003,48(6):988-1001.
[21]Boukas E K Haurie A. "Manufacturing flow control and preventive maintenance:a s-tochastic control approach[J]." IEEE Transactions on Automatic Control,1990,35(7):10 24-1031.
[22]Ren W, Beard R. Consensus seeking in multi-agent systems under dynamically chang-ing interaction topologies. IEEE Transactions on Automatic Control,2005,50(5):655-661.
[23]Li S, Wang J, Luo X, et al. A new framework of consensus protocol design for complex multi-agent systems. Systems and Control Letters,2011,60(1):19-26.
[24]Li Z, Liu X, Lin P, et al. Consensus of linear multi-agent systems with reduced-order observer-based protocols. Systems and Control Letters,2011.
[25]Gu K.Kharitonov L,Chen J. "Stability of Time-delay Systems[M]." Boston:Birkhauser, 2003.
[26]Niculescu S I. "Delay Effects on Stability:A Robust Control Approach[M]." Berlin:Sprin-ger,2001.
[27]Ren W, Beard R. Consensus seeking in multi-agent systems under dynamically chang-ing interaction topologies. IEEE Transactions on Automatic Control,2005,50(5):655-661.
[28]俞立.鲁棒控制[M].清华大学出版社,2002
[29]吴敏,何勇.时滞系统鲁棒控制——自由权矩阵方法[M].北京：科学出版社,2008
[30]苏宏业,褚健,鲁仁全,稽小辅.不确定时滞系统的鲁棒控制理论[M].北京：科学出版社,2007.
[31]Chen W H,Xu J X,Guan Z H, "Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delaysl [J]." IEEE Transactions on Automatic Control.2003,48:2270-2277.
[32]Wang Z,Liu X, "Exponential stabilization of a class of stochastic system with Marko-vian jump parameters and mode-dependent mixed time-delays [J]. " IEEE Transac-tions on Automatic Control.2010,55(7):1656-1662.
[33]Dong H,Wang Z,Ho D,et al. "Robust H filtering for Markovian jump systems with ran-domly occurring nonlinearities and sensor saturation:The finite-horizon case[J]." IEEE Transactions on Signal Processing,2011,59(7):3048-3057.
[34]Zhang L,Boukas E K. "Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities[J].Automatica,2009,45(2):463-468.
[35]M. Baglietto, T. Parisini, and R. Zoppoli, "Distributed-information neural control: The case of dynamic routing in traffic networks," IEEE Trans. Neural Networks, vol. 12, no.3, pp.485-502, May 2001.
[36]Zhang L,Boukas E,Lam J. "Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities[J]. " IEEE Transac-tions on Automatic Control,2008,53(10):2458-2464.
[37]Xiong J, Lam J, Gao H, et al."On robust stabilization of Markovian jump sys-tems with uncertain switching probabilities [J]".Automatica,2005,41(5):897-903. Automatica,2005,41(5):897-903.
[38]Zhang L,Boukas E, "Mode-dependent H∞, filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilitiesl [J]. " Automatica,2009,45 (6):1462-1467.
[2]F. Abdollahi and K. Khorasani, "A novel H∞ control strategy for design of a robust dynamic routing algorithm in traffic networks," IEEE Journal on Selected Areas in Communications, vol.26, no.4, pp.706-718,2008.
[3]Xueming Si, Xun-Lin Zhu, Xin Du, and Xiangpeng Xie, "A decentralized routing control scheme for data communication networks." Mathematical Problems in Engi-neering.
[4]N. Chen, X. Zhang, and W. Gui, "Robust decentralized H∞ control of multi-channel uncertain time-delay systems:An LMI approach." Proceedings of IEEE International Conference on Mechatronics and Automation, pp.367-372,2006.
[5]Kokmae H, Kobayashi H, Mori T. "Robust Performance for Linear Delay-differential Systems with Time-varying Uncertainties [J]." IEEE AC(S0018-9286).1998,43(7):971-974
[6]杨柳,多智能体分布式协调控制,硕士学位论文,中山大学,2009.
[7]孙凤兰,多智能体网络的一致性研究,博士学位论文,华中科技大学,2012.
[8]吴正平.复杂网络建模与一致性及在多移动智能体中的应用：[PhD Dissertation].华中科技大学,2007.
[9]汪小帆,李翔,陈关荣.复杂网络理论及其应用.清华大学出版社,2006.
[10]刘智伟.基于混杂控制的复杂多智能体网络同步一致性研究：[PhD Dissertation].华中科技大学,2011.
[11]K. Gu, "An integral inequality in the stability problem of time-delay systems." Pro-ceedings of 39th IEEE Conference on Decision and Control,2000, pp.2805-2810.
[12]X. Zhu and Y. Wang, "Parameter-dependent switching law for linear switched sys-tems with time-varying delay." Proceedings of 9th IEEE International Con-ference on Control and Automation, pp.300-305,2011.
[13]Mahmoud M S, Shi P. "Methodologies for Control of Jump Time-Delay Systems[M]." Kluwer Academic Publishers.2003.
[14]Xue F, Kumar P. The number of neighbors needed for connectivity of wireless net-works.Wireless networks,2004,10(2):169-181.
[15]Mao X. "Stochastic Differential Equations and Their Applications[M]."Chichester. Honvood,1997.
[16]Boukas E. "Hoo control of discrete-time Markov jump systems with bounded transi-tion probabilities[J]. "Optimal Control Applications and Methods,2009,30(5):477-494.
[17]Fang Y G Loparo K A. "Stabilization of continuous time jump linear systems[J]." IEEE Transactions on Automatic Control,2002,47(10):1590.1630.
[18]Boukas E K,Shi P,Nguang S K. "Robust H∞ control for linear markov jump systems with unknow nonlinearties[J]." Journal of Mathematical Analysis and Applications, 2003,282(1):241-255.
[19]Krasovskii N N,Lidskii E A. "Analytical design of controllers in systems with random arributes[J]." Automation and Remote Control,1961,22:1021-1025.
[20]Jadbabaie A, Lin J, Morse A. Coordination of groups of mobile autonomous agents us-ing nearest neighbor rules. IEEE Transactions on Automatic Control,2003,48(6):988-1001.
[21]Boukas E K Haurie A. "Manufacturing flow control and preventive maintenance:a s-tochastic control approach[J]." IEEE Transactions on Automatic Control,1990,35(7):10 24-1031.
[22]Ren W, Beard R. Consensus seeking in multi-agent systems under dynamically chang-ing interaction topologies. IEEE Transactions on Automatic Control,2005,50(5):655-661.
[23]Li S, Wang J, Luo X, et al. A new framework of consensus protocol design for complex multi-agent systems. Systems and Control Letters,2011,60(1):19-26.
[24]Li Z, Liu X, Lin P, et al. Consensus of linear multi-agent systems with reduced-order observer-based protocols. Systems and Control Letters,2011.
[25]Gu K.Kharitonov L,Chen J. "Stability of Time-delay Systems[M]." Boston:Birkhauser, 2003.
[26]Niculescu S I. "Delay Effects on Stability:A Robust Control Approach[M]." Berlin:Sprin-ger,2001.
[27]Ren W, Beard R. Consensus seeking in multi-agent systems under dynamically chang-ing interaction topologies. IEEE Transactions on Automatic Control,2005,50(5):655-661.
[28]俞立.鲁棒控制[M].清华大学出版社,2002
[29]吴敏,何勇.时滞系统鲁棒控制——自由权矩阵方法[M].北京：科学出版社,2008
[30]苏宏业,褚健,鲁仁全,稽小辅.不确定时滞系统的鲁棒控制理论[M].北京：科学出版社,2007.
[31]Chen W H,Xu J X,Guan Z H, "Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delaysl [J]." IEEE Transactions on Automatic Control.2003,48:2270-2277.
[32]Wang Z,Liu X, "Exponential stabilization of a class of stochastic system with Marko-vian jump parameters and mode-dependent mixed time-delays [J]. " IEEE Transac-tions on Automatic Control.2010,55(7):1656-1662.
[33]Dong H,Wang Z,Ho D,et al. "Robust H filtering for Markovian jump systems with ran-domly occurring nonlinearities and sensor saturation:The finite-horizon case[J]." IEEE Transactions on Signal Processing,2011,59(7):3048-3057.
[34]Zhang L,Boukas E K. "Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities[J].Automatica,2009,45(2):463-468.
[35]M. Baglietto, T. Parisini, and R. Zoppoli, "Distributed-information neural control: The case of dynamic routing in traffic networks," IEEE Trans. Neural Networks, vol. 12, no.3, pp.485-502, May 2001.
[36]Zhang L,Boukas E,Lam J. "Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities[J]. " IEEE Transac-tions on Automatic Control,2008,53(10):2458-2464.
[37]Xiong J, Lam J, Gao H, et al."On robust stabilization of Markovian jump sys-tems with uncertain switching probabilities [J]".Automatica,2005,41(5):897-903. Automatica,2005,41(5):897-903.
[38]Zhang L,Boukas E, "Mode-dependent H∞, filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilitiesl [J]. " Automatica,2009,45 (6):1462-1467.