一类基于切换的非线性网络控制系统的控制研究
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摘要
网络控制系统(NCS,Networked Control System)是指传感器、控制器和执行器机构通过通信网络形成闭环的控制系统。在网络控制系统中,网络成为一种媒介实现分属于不同区域里的系统部件之间的信息交换和控制信号的传递。因此网络控制系统中的丢包,时延和不确定性使得这方面的研究十分复杂。
本文主要基于切换技术对一类非线性网络控制系统进行了模型建立、鲁棒分析和最优控制。主要结果如下:
首先介绍了网络控制系统的产生与发展过程以及研究内容和研究现状及其存在的问题,之后简述了切换系统的研究和发展。
其次研究了一类非线性系统简单的短时延、单包传输条件下丢包的数学模型。然后逐步得出此类非线性过程长时延、多包传输条件下丢包的系统的数学模型,为以后的分析、仿真和控制器设计奠定了基础。
再次考虑了系统中存在种种不确定性的情况下,如何保持切换系统的稳定性。通过研究,得到文中所研究系统在任意切换条件下保证不确定网络控制系统的鲁棒二次稳定性的条件,仿真结果验证了本文所提方法的正确性和有效性。
最后分析了Markov特性的短时延非线性网络控制系统的镇定,首先建立了数学模型,根据模型,设计了使得闭环系统稳定的状态反馈和输出反馈控制器,并研究其稳定性问题;仿真结果验证了本文所提方法的正确性和有效性。然后分析了Markov特性的长时延非线性网络控制系统的最优控制,建立了数学模型,根据模型进行了随机最优控制研究。
Network Control System (NCS, Networked Control System) is a closed-loop communication network control system which composed and operated by sensor, controller and actuator .In the network control system, the network serves as a medium to achieve the exchange of signal and data between system components and control signals which are arranged in different regions. Packet loss, transmit delay, and uncertainty are normal phenomenon in network control system, therefore the research of NCS is very complicated.
Based on switching technology, this paper build a model for a class of nonlinear networked control system, then analysis the robust and optimal control characteristic of the model.The main results are as follows:
Firstly, this paper introduces the production and research development of network control system, the status of current research and problems needed to be improved, and briefly illustrate the research and development of switched systems.
Secondly, study the simple short delay and packet loss under a single packet transmission in the model of a class of nonlinear systems. Through these research this paper propose the model for network control system under the condition of long delay and packet loss over many packets, this is the foundation of the subsequent analysis, simulation and controller design .
Thirdly, considering the system uncertainties exist in many cases, therefore it is critical to maintain the stability of switched systems. Through research, this paper concludes the conditions which make sure the robust quadratic stability of uncertain networked control systems stability under arbitrary switching cases.
Finally, in order to analysis the stabilization of Markov properties short delayed nonlinear network control systems, this paper first build a mathematical model of the system, then based on the model this paper designed state feedback and output feedback controllers which can keep the stable of the closed-loop system. The simulation results demonstrate the validity and effectiveness of the proposed method. This paper also analyzed the optimal control of Markov properties long-delay nonlinear networked control systems, build a mathematical model and study the stochastic optimal control of the model.
本文主要基于切换技术对一类非线性网络控制系统进行了模型建立、鲁棒分析和最优控制。主要结果如下:
首先介绍了网络控制系统的产生与发展过程以及研究内容和研究现状及其存在的问题,之后简述了切换系统的研究和发展。
其次研究了一类非线性系统简单的短时延、单包传输条件下丢包的数学模型。然后逐步得出此类非线性过程长时延、多包传输条件下丢包的系统的数学模型,为以后的分析、仿真和控制器设计奠定了基础。
再次考虑了系统中存在种种不确定性的情况下,如何保持切换系统的稳定性。通过研究,得到文中所研究系统在任意切换条件下保证不确定网络控制系统的鲁棒二次稳定性的条件,仿真结果验证了本文所提方法的正确性和有效性。
最后分析了Markov特性的短时延非线性网络控制系统的镇定,首先建立了数学模型,根据模型,设计了使得闭环系统稳定的状态反馈和输出反馈控制器,并研究其稳定性问题;仿真结果验证了本文所提方法的正确性和有效性。然后分析了Markov特性的长时延非线性网络控制系统的最优控制,建立了数学模型,根据模型进行了随机最优控制研究。
Network Control System (NCS, Networked Control System) is a closed-loop communication network control system which composed and operated by sensor, controller and actuator .In the network control system, the network serves as a medium to achieve the exchange of signal and data between system components and control signals which are arranged in different regions. Packet loss, transmit delay, and uncertainty are normal phenomenon in network control system, therefore the research of NCS is very complicated.
Based on switching technology, this paper build a model for a class of nonlinear networked control system, then analysis the robust and optimal control characteristic of the model.The main results are as follows:
Firstly, this paper introduces the production and research development of network control system, the status of current research and problems needed to be improved, and briefly illustrate the research and development of switched systems.
Secondly, study the simple short delay and packet loss under a single packet transmission in the model of a class of nonlinear systems. Through these research this paper propose the model for network control system under the condition of long delay and packet loss over many packets, this is the foundation of the subsequent analysis, simulation and controller design .
Thirdly, considering the system uncertainties exist in many cases, therefore it is critical to maintain the stability of switched systems. Through research, this paper concludes the conditions which make sure the robust quadratic stability of uncertain networked control systems stability under arbitrary switching cases.
Finally, in order to analysis the stabilization of Markov properties short delayed nonlinear network control systems, this paper first build a mathematical model of the system, then based on the model this paper designed state feedback and output feedback controllers which can keep the stable of the closed-loop system. The simulation results demonstrate the validity and effectiveness of the proposed method. This paper also analyzed the optimal control of Markov properties long-delay nonlinear networked control systems, build a mathematical model and study the stochastic optimal control of the model.
引文
[1] W Zhang, M. S. Branicky, S. M. Phillips. Stability of networked control systems. IEEE Control System Magazine, 2001, 21(1):84~99.
[2] Nillsonn, Bernhardsson B, Wittermark B. Stochastic analysis and control of real-time systems with random time delays. Automatica, 1998, 34(1): 57~64
[3] Nillsonn. Real-time control systems with delays. Lund, Swe2den: Department Automatic Control, Lund Institute of Technology, 1998
[4] R. Krtokica, U. Ozguner, H. Chan, H. Goktas, J. Winkelman and M. Liubakka. Stability of linear feedback systems with random communication delays. International Journal of Control, 1994, 59 (4), 925~953,
[5] Lian F L,Moyne J, Tilbury D. Analysis and modeling of networked control systems:MIMO case with multiple time delays. Arlington, USA: Proceeding of the American Control Conference, 2001
[6] Lian F L, Moyne J, Tilbury D. Optimal controller design and evaluation for a class of networked control systems with distributed constant delay. Alaska, USA: Proceeding of the American Control Conference, 2002.
[7] Lineoln B, Bernhardsson B. Optional Control over networks with long random delay. In Proc. of the International Symposium on Mathematical Theory of Networks and systems, 2000
[8] Xiao L, Hassibi A, How JP. Control with random communication delays via a discrete time jump systems approach [A]. Proceedings of the 2000 American Control Conference. Chicago, USA: IEEE, 2000: 2199~2204.
[9]朱其新,胡寿松.网络控制系统的分析与建模.信息与控制,2003,21(1):5~8
[10] Hai L,Guisheng Z,Panos J A.Ranos stability and disturbance attenuation analysis of a class of networked control systems.Proc 42rd IEEE Conference on Decision and Control,Maui,Hawaii USA,2003:1182~1187
[11] Lin H,Antsaklis P J.Persistent disturbance attenuation properties for networked control systems.43rd IEEE Conference on Decision and Control,Atlantis,Paradise Island,Bahamas,2004:953~958.
[12] D. Ma,J.Zhao.Stabilization of networked control systems via switching controllers: an average dwell time approach, Intelligent Control and Automation, 2006. WCICA 2006. 2006,1: 4619~4622.
[13] J.Huang,Z.H.Guan,Z.D.Wang.Robust control with performance bound for networked control systems with data packet dropouts, Control and Decision, 2005, 20:1002~1005.
[14]白涛,吴智铭,杨根科.w网络化控制制系统中的抖动优化调度算法.控制与决策,2004,19(4):397~401
[15]何坚强,张焕春.基于遗传算法的网络化控制系统优化调度研究.工业仪表与自动化装置,2004, 12(4):37~39,
[16] R. Alur, T. A. Henziner, E. D. Sontag. Hybrid systems III-Verification and Control. Volume 1066 of Lecture Notes in Computer Science Springer, 1996.
[17] P. J. Antsklis. Proceedings of the IEEE-special Issue on Hybrid Applications. 2000, 88(12).
[18]莫以为,萧德云.混合动态系统及其应用综述.控制理论与应用,2002,19(1):1~8.
[19]曾锋.离散混杂系统的建模和控制方法研究.北京:中国科学院自动化研究所博士学位论文,2005.
[20] Billings K. Switchmode Power Supply Handbook, New York: McGraw-Hill, 1989.
[21]邵振明.基于切换的一类网络控制系统的分析与设计.东北大学硕士学位论文, 2006.
[22]付主木,费树铭,高爱云.切换系统的H∞控制.北京:科学出版社, 2009.
[23] Peleties P,Decarlo R A.Asymptomatic stability of M-switched using Lyapunov function. Proceedings of Conference on Decision and Control,Tucson,1992:3438~3439.
[24] Branicky M S. Multiple Lyapunov functions and other analysis tools for switched and hybrid system, IEEE Trans. Automat. Contr., 1998, 43(4): 475~482.
[25] Ye H, Michel A N, Hou L. Stability theory for hybrid dynamical systems, IEEE Trans.Automat. Contr., 1998, 43(4): 461~474.
[26] Shorten R N, Narendra K S,Mason O.On common quadratic Lyapunov functions for pares of stable LTI system whose systems matrices are in companion form. IEEE Transactions on Automatic Control,2003,48(4):618~621.
[27] Zhai G S,Xu X P,Lin H et al.An extension of lie algebraic stability analysis for switched systems with continuous-time a discrete-time subsystems. Proceedings of the IEEE International Conference on Networking,Sensing and Control,Ft.Lauderdale,2006:362~367
[28] Ezzine J,Haddad A H.Controllability and observability of hybrid systems. International Journal of Control,1989,49(6):2045~2055.
[29] Blondel V D,Tsitsiklis J N.Complexity of stability and controllability of elementary hybrid systems.Automatica,1999,35(3):479~489.
[30] Sun Z D, Ge S S, Lee T H. Controllability and reachability criteria for switched linear systems, Automatica,38(5): 775~786.
[31] Perterson S,Lennarton B.Stability and robustness for hybrid systems.Proceedings of the 35th Conference on Decision and Control,Kobe,1996,2,1202~1207.
[32] Wang Z N,Fei S M,Feng C B.Robustness analysis and robust control for a class of hybrid system.Control Theory and Application,2001,18(3):375~379.
[33] Wick M A, Peleties P, DeCarlo R A. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems, European J. Contr., 1998, 4(1):140~147.
[34] Michel A N. Recent trends in the stability analysis of hybrid dynamical systems, IEEETrans.Circuits Syst. I, 1999, 46(1): 120~134.
[35] Wick M A, Peleties P, DeCarlo R A. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems, European J. Contr., 1998, 4(1):140~147.
[36] Li Z G, Wen C Y, Soh Y C. Observer-based stabilization of switching linear systems, Automatics, 2003, 39(3): 517~524.
[37] Xie G M, Wang L. Controllability and stabilizability of switched linear-systems, Systems&Control Letters, 2003, 48(2): 135~155.
[38] Riedinger P, Kratz F, Iung C, Zanne C. Linear quadratic optimization for hybrid systems, In:Proceedings of the 38th Conference on Decision&Control, Phoenix, Arizona: Qmnipress, 1999, 3359~3364.
[39] T. Mori, N. Fukuma, M. Kuwahare. On an estimate of the decay rate for stable linear delay systems.International Journal of Control, 1982, 36(1): 95~97.
[40] D. D. Liberzon, A. S. Morse. Basic problems in stability and design of switched systems. IEEE Control Syst. Mag., 1999, (19): 59~70.
[41] Ji,Y.,Chizeck,H.J.,Feng X., and Loparo, K. Stability and Control of Discrete-time Jump Linear Systems. Control Theory and Advanced Technology, 1991,7(2): 247~270.
[42]朱其新,胡寿松,刘亚.无限时间长时延网络控制系统的随机最优控制.控制理论与应用,Jun2004,21(3):321~326.
[43] Astrom K., J Introduction to stochastic control theory. New York: Academic Press,1970[69].
[44] Li X, de Souza C E. Delay-dependent robust H∞control of uncertain linear state-delayed systems. Automatica, 1999,35: 1313~1321.
[45] Hespanha J P, Naghshtabrizi P, Xu Y G. A survey of recent results in networked control systems. Proceedings of the IEEE, 2007, 95(1): 138~162.
[46] Wang Z D, Yang F W, Daniel W C H, Liu X H. Robust H∞control for networked systems with random packet losses.IEEE Transactions on Systems, Man, and Cybernetics, PartB: Cybernetics, 2007, 37(4): 916~924.
[47] Xiong J L, James L. Stabilization of linear systems over networks with bounded packet loss. Automatica, 2007, 43(1):80~87.
[48] Yang F W, Wang Z D, Hung Y S, Gani M. H∞control for networked systems with random communication delays. IEEE Transactions on Automatic Control, 2006, 51(3):511~518.
[49] Yan H S, Huan X H, Wang M, Zhang H. Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output. Chaos, Soliton and Fractals,2007, 34: 997~1005.
[50] Wen-An Zhang, Li Yu,A robust control approach to stabilization of networked control systems with time-varying delays,Automatica,2009,10(10):2440-2445.
[51] Jia X C, Zhang D W, Zheng L H, Zheng N N. Modeling and stabilization for a class of nonlinear networked control systems: a T-S fuzzy approach. Progress in atural Science,2008, 18(8): 1031~1037.
[52] Liu Y Z, Yu H B. Stability of network control systems based on switched technique. In: Proceedings of the 42nd IEEE conference on decision and control. Hawaii, USA: IEEE,2003. 1110~1113.
[53] Zhang W A, Yu L. Output feedback stabilization of networked control systems with packet dropouts. IEEE Transactions on Automatic Control, 2007, 52(9): 705~710.
[54] Xie D, Chen X, Lv L, Xu N. Asymptotical stabilisability of networked control systems: time-delay switched system approach. IET Proceeding-Control Theory and Applications,2008, 2(9): 743~751.
[55] Zhi-Hong Guan, Hao Zhang, Shuang-Hua Yang,Robust passive control for Internet-based switching systems with time-delay,Chaos, Solitons & Fractals, 2008.4(2):479~486.
[56]杨绪,王向东.网络控制系统的稳定性分析.2004中国控制与决策学术年会.2004, 5.
[57]杨裙,王向东.一类带有不确定性的网络控制系统的稳定性分析.沈阳工业大学学报.2004,
[58] Ilia G. Polushin, Peter X. Liu, Chung-Horng Lung,On the model-based approach to nonlinear networked control systems,Automatica, 2008.9(9), :2409~2414.
[59] C. Popescu, Y Wang, H. Zhuang, Stability of Delayed Networked Nonlinear Systems, Proceeding of the16th Florida Conference on the Recent Advances in Robotics, 2003.
[60] Jian Guo Li, Jing Qi Yuan, Jun Guo Lu.Observer-based H∞control for networked nonlinear systems with random packet losses, ISA Transactions,2010, 1(1):39~46.
[2] Nillsonn, Bernhardsson B, Wittermark B. Stochastic analysis and control of real-time systems with random time delays. Automatica, 1998, 34(1): 57~64
[3] Nillsonn. Real-time control systems with delays. Lund, Swe2den: Department Automatic Control, Lund Institute of Technology, 1998
[4] R. Krtokica, U. Ozguner, H. Chan, H. Goktas, J. Winkelman and M. Liubakka. Stability of linear feedback systems with random communication delays. International Journal of Control, 1994, 59 (4), 925~953,
[5] Lian F L,Moyne J, Tilbury D. Analysis and modeling of networked control systems:MIMO case with multiple time delays. Arlington, USA: Proceeding of the American Control Conference, 2001
[6] Lian F L, Moyne J, Tilbury D. Optimal controller design and evaluation for a class of networked control systems with distributed constant delay. Alaska, USA: Proceeding of the American Control Conference, 2002.
[7] Lineoln B, Bernhardsson B. Optional Control over networks with long random delay. In Proc. of the International Symposium on Mathematical Theory of Networks and systems, 2000
[8] Xiao L, Hassibi A, How JP. Control with random communication delays via a discrete time jump systems approach [A]. Proceedings of the 2000 American Control Conference. Chicago, USA: IEEE, 2000: 2199~2204.
[9]朱其新,胡寿松.网络控制系统的分析与建模.信息与控制,2003,21(1):5~8
[10] Hai L,Guisheng Z,Panos J A.Ranos stability and disturbance attenuation analysis of a class of networked control systems.Proc 42rd IEEE Conference on Decision and Control,Maui,Hawaii USA,2003:1182~1187
[11] Lin H,Antsaklis P J.Persistent disturbance attenuation properties for networked control systems.43rd IEEE Conference on Decision and Control,Atlantis,Paradise Island,Bahamas,2004:953~958.
[12] D. Ma,J.Zhao.Stabilization of networked control systems via switching controllers: an average dwell time approach, Intelligent Control and Automation, 2006. WCICA 2006. 2006,1: 4619~4622.
[13] J.Huang,Z.H.Guan,Z.D.Wang.Robust control with performance bound for networked control systems with data packet dropouts, Control and Decision, 2005, 20:1002~1005.
[14]白涛,吴智铭,杨根科.w网络化控制制系统中的抖动优化调度算法.控制与决策,2004,19(4):397~401
[15]何坚强,张焕春.基于遗传算法的网络化控制系统优化调度研究.工业仪表与自动化装置,2004, 12(4):37~39,
[16] R. Alur, T. A. Henziner, E. D. Sontag. Hybrid systems III-Verification and Control. Volume 1066 of Lecture Notes in Computer Science Springer, 1996.
[17] P. J. Antsklis. Proceedings of the IEEE-special Issue on Hybrid Applications. 2000, 88(12).
[18]莫以为,萧德云.混合动态系统及其应用综述.控制理论与应用,2002,19(1):1~8.
[19]曾锋.离散混杂系统的建模和控制方法研究.北京:中国科学院自动化研究所博士学位论文,2005.
[20] Billings K. Switchmode Power Supply Handbook, New York: McGraw-Hill, 1989.
[21]邵振明.基于切换的一类网络控制系统的分析与设计.东北大学硕士学位论文, 2006.
[22]付主木,费树铭,高爱云.切换系统的H∞控制.北京:科学出版社, 2009.
[23] Peleties P,Decarlo R A.Asymptomatic stability of M-switched using Lyapunov function. Proceedings of Conference on Decision and Control,Tucson,1992:3438~3439.
[24] Branicky M S. Multiple Lyapunov functions and other analysis tools for switched and hybrid system, IEEE Trans. Automat. Contr., 1998, 43(4): 475~482.
[25] Ye H, Michel A N, Hou L. Stability theory for hybrid dynamical systems, IEEE Trans.Automat. Contr., 1998, 43(4): 461~474.
[26] Shorten R N, Narendra K S,Mason O.On common quadratic Lyapunov functions for pares of stable LTI system whose systems matrices are in companion form. IEEE Transactions on Automatic Control,2003,48(4):618~621.
[27] Zhai G S,Xu X P,Lin H et al.An extension of lie algebraic stability analysis for switched systems with continuous-time a discrete-time subsystems. Proceedings of the IEEE International Conference on Networking,Sensing and Control,Ft.Lauderdale,2006:362~367
[28] Ezzine J,Haddad A H.Controllability and observability of hybrid systems. International Journal of Control,1989,49(6):2045~2055.
[29] Blondel V D,Tsitsiklis J N.Complexity of stability and controllability of elementary hybrid systems.Automatica,1999,35(3):479~489.
[30] Sun Z D, Ge S S, Lee T H. Controllability and reachability criteria for switched linear systems, Automatica,38(5): 775~786.
[31] Perterson S,Lennarton B.Stability and robustness for hybrid systems.Proceedings of the 35th Conference on Decision and Control,Kobe,1996,2,1202~1207.
[32] Wang Z N,Fei S M,Feng C B.Robustness analysis and robust control for a class of hybrid system.Control Theory and Application,2001,18(3):375~379.
[33] Wick M A, Peleties P, DeCarlo R A. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems, European J. Contr., 1998, 4(1):140~147.
[34] Michel A N. Recent trends in the stability analysis of hybrid dynamical systems, IEEETrans.Circuits Syst. I, 1999, 46(1): 120~134.
[35] Wick M A, Peleties P, DeCarlo R A. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems, European J. Contr., 1998, 4(1):140~147.
[36] Li Z G, Wen C Y, Soh Y C. Observer-based stabilization of switching linear systems, Automatics, 2003, 39(3): 517~524.
[37] Xie G M, Wang L. Controllability and stabilizability of switched linear-systems, Systems&Control Letters, 2003, 48(2): 135~155.
[38] Riedinger P, Kratz F, Iung C, Zanne C. Linear quadratic optimization for hybrid systems, In:Proceedings of the 38th Conference on Decision&Control, Phoenix, Arizona: Qmnipress, 1999, 3359~3364.
[39] T. Mori, N. Fukuma, M. Kuwahare. On an estimate of the decay rate for stable linear delay systems.International Journal of Control, 1982, 36(1): 95~97.
[40] D. D. Liberzon, A. S. Morse. Basic problems in stability and design of switched systems. IEEE Control Syst. Mag., 1999, (19): 59~70.
[41] Ji,Y.,Chizeck,H.J.,Feng X., and Loparo, K. Stability and Control of Discrete-time Jump Linear Systems. Control Theory and Advanced Technology, 1991,7(2): 247~270.
[42]朱其新,胡寿松,刘亚.无限时间长时延网络控制系统的随机最优控制.控制理论与应用,Jun2004,21(3):321~326.
[43] Astrom K., J Introduction to stochastic control theory. New York: Academic Press,1970[69].
[44] Li X, de Souza C E. Delay-dependent robust H∞control of uncertain linear state-delayed systems. Automatica, 1999,35: 1313~1321.
[45] Hespanha J P, Naghshtabrizi P, Xu Y G. A survey of recent results in networked control systems. Proceedings of the IEEE, 2007, 95(1): 138~162.
[46] Wang Z D, Yang F W, Daniel W C H, Liu X H. Robust H∞control for networked systems with random packet losses.IEEE Transactions on Systems, Man, and Cybernetics, PartB: Cybernetics, 2007, 37(4): 916~924.
[47] Xiong J L, James L. Stabilization of linear systems over networks with bounded packet loss. Automatica, 2007, 43(1):80~87.
[48] Yang F W, Wang Z D, Hung Y S, Gani M. H∞control for networked systems with random communication delays. IEEE Transactions on Automatic Control, 2006, 51(3):511~518.
[49] Yan H S, Huan X H, Wang M, Zhang H. Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output. Chaos, Soliton and Fractals,2007, 34: 997~1005.
[50] Wen-An Zhang, Li Yu,A robust control approach to stabilization of networked control systems with time-varying delays,Automatica,2009,10(10):2440-2445.
[51] Jia X C, Zhang D W, Zheng L H, Zheng N N. Modeling and stabilization for a class of nonlinear networked control systems: a T-S fuzzy approach. Progress in atural Science,2008, 18(8): 1031~1037.
[52] Liu Y Z, Yu H B. Stability of network control systems based on switched technique. In: Proceedings of the 42nd IEEE conference on decision and control. Hawaii, USA: IEEE,2003. 1110~1113.
[53] Zhang W A, Yu L. Output feedback stabilization of networked control systems with packet dropouts. IEEE Transactions on Automatic Control, 2007, 52(9): 705~710.
[54] Xie D, Chen X, Lv L, Xu N. Asymptotical stabilisability of networked control systems: time-delay switched system approach. IET Proceeding-Control Theory and Applications,2008, 2(9): 743~751.
[55] Zhi-Hong Guan, Hao Zhang, Shuang-Hua Yang,Robust passive control for Internet-based switching systems with time-delay,Chaos, Solitons & Fractals, 2008.4(2):479~486.
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