两类网络化控制系统的研究
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摘要
本文研究两类网络化控制系统.一类是在信息受限条件下基于观测器的连续混沌系统的同步.对于具有混沌形式的驱动系统和基于观测器的响应系统,通过一个有限容量的信道连接,设计有效的量化方法使得同步误差关于传输误差是输入到状态稳定(简记为ISS),同时传输误差是指数稳定.因此,在有限信道容量的条件下同步误差渐近趋于零.本文结果克服了以往研究工作在有限传输能力情况下无法使得同步误差渐近趋于零的缺陷.仿真例子也验证了本文方法的有效性.
另一类是对具有时变传输周期的正则,无脉冲的广义网络化控制系统进行分析,其中传感器采用时钟驱动,控制器和执行器采用时间驱动.在无传输时延和数据丢包的情况下,广义网络化控制系统可转化为异步动态系统,同时将时变传输周期变量视为参数不确定项.进而利用李雅普诺夫方法和线性矩阵不等式的技巧,给出系统指数稳定的充要条件.利用Matlab LMI工具箱,本文所采用的方法不仅可以判定广义网络化系统的稳定性,而且还可以获得使系统指数稳定的状态反馈控制律.最后仿真例子验证了方法的可行性.
In this paper, two classes of networked control systems are studied. The first one is an observer-based synchronization of a continuous chaotic system under information constraints. For a general chaotic master system and its observer-based slave system, which are connected by a limited capacity channel, a practical quantized scheme is designed such that the synchronization error is ISS on the transmission error, while the transmission error converges to zero exponentially. Therefore, the synchronization error converges to zero asymptotically under information constraints. The obtained result overcomes difficulties of previous works in which the synchronization error can't converge to zero under information constraints. Finally, a simulation example is presented to illustrate the result.
The second one is a regular and impulsive-free singular networked control system, where the sensor node is time-driven, but the controller and executor are event-driven. Then, such a singular networked control system can be modeled as an asynchronous dynamical system in the case of no networked-induced delay and no data packet dropout. Meanwhile, being regarded a time-varying transmission period as a time-varying uncertain parameter, a sufficient condition on exponential stability is given by the Lyapunov function method and LMI (linear matrix inequality) techniques. Taking advantage of the Matlab LMI toolbox, we can not only prove the stability of the networked system, but also construct a state feedback control law. A simulation example is given to illustrate the relevant result.
另一类是对具有时变传输周期的正则,无脉冲的广义网络化控制系统进行分析,其中传感器采用时钟驱动,控制器和执行器采用时间驱动.在无传输时延和数据丢包的情况下,广义网络化控制系统可转化为异步动态系统,同时将时变传输周期变量视为参数不确定项.进而利用李雅普诺夫方法和线性矩阵不等式的技巧,给出系统指数稳定的充要条件.利用Matlab LMI工具箱,本文所采用的方法不仅可以判定广义网络化系统的稳定性,而且还可以获得使系统指数稳定的状态反馈控制律.最后仿真例子验证了方法的可行性.
In this paper, two classes of networked control systems are studied. The first one is an observer-based synchronization of a continuous chaotic system under information constraints. For a general chaotic master system and its observer-based slave system, which are connected by a limited capacity channel, a practical quantized scheme is designed such that the synchronization error is ISS on the transmission error, while the transmission error converges to zero exponentially. Therefore, the synchronization error converges to zero asymptotically under information constraints. The obtained result overcomes difficulties of previous works in which the synchronization error can't converge to zero under information constraints. Finally, a simulation example is presented to illustrate the result.
The second one is a regular and impulsive-free singular networked control system, where the sensor node is time-driven, but the controller and executor are event-driven. Then, such a singular networked control system can be modeled as an asynchronous dynamical system in the case of no networked-induced delay and no data packet dropout. Meanwhile, being regarded a time-varying transmission period as a time-varying uncertain parameter, a sufficient condition on exponential stability is given by the Lyapunov function method and LMI (linear matrix inequality) techniques. Taking advantage of the Matlab LMI toolbox, we can not only prove the stability of the networked system, but also construct a state feedback control law. A simulation example is given to illustrate the relevant result.
引文
[1]胡刚,萧井华,郑志刚,混沌控制,上海,上海教育出版社,2000.
[2]陈关荣,吕金虎,Lorenz系统族的动力学行为,控制与同步,北京,科学出版社,2003.
[3]E. Ott, C. Grebogi and J. A. Yorke, Controlling chaos, Phys. Rev. Lett.,64,1990, pp.1196-1199.
[4]Alexander L. Fradkov, Boris Andrievsky and Robin J. Evans, Chaotic observer-based synchronization under information constraints, Physical Review E 73,066209,2006.
[5]Alexander L. Fradkov, Boris Andrievsky and Robin J. Evans, Adaptive Observer-Based Synchronization of Chaotic Systems with First-Order Coder in the Presence of Information Constraints, IEEE Tran. on Circuits and Systems-Ⅰ Regular Paper, vol.55 (6),2008, pp.1685-1694.
[6]Alexander L. Fradkov, Boris Andrievsky and Robin J. Evans, Controlled synchronization under information constraints, Physical Review E 78,036210, 2008.
[7]Gexia Wang, Zhiming Wang and Guoping Lu, Chaotic synchronization with limited information, Int. J. of Bifurcation and chaos, vol.18 (10),2008, pp.1-9.
[8]A. Savkin, Detectability and output feedback stabilizability of nonlinear networked control systems, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, pp. 8174-8178,2005.
[9]A.L. Fradkov, B. Andrievsky and R. J. Evans, Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints, Math. OC, Dec 2007, pp.1-8.
[10]A.L. Fradkov, B. Andrievsky, Observer-Based Synchronization of Discrete-time Chaotic Systems under Communication Constraints, IFAC, July 2008, pp. 3719-3724.
[11]Hassan K. Khalil, Nonlinear Systems [M],2005:125-130
[12]Guang-Da Hu, Observers for one sided Lipschitz non-Linear systems [J], Journal of Mathematical Control and Information.2006(23):395-401.
[13]Daniel Liberzon and Dragan Nesic, Input-to State Stabilization of Linear Systems with Quantized State Measurements [C], IEEE Trans. Auto. Control, Vol.52, No.5,2007, pp.767-781.
[14]L.Y. Zhao, X. R. Li and G. R. Zhao, Chaotic Synchronization Based on Riccati Inequality with Application to Secure Communication [C], IEEE Trans. Auto. Control, July 2004, pp.1308-1311.
[15]R. W. Brockett and D. Liberzon, Quantized Feedback of Linear Systems, IEEE Trans. Auto. Control, Vol.45, No.7, July 2000, pp.1279-1289:
[16]W. S. Wong and W. Brockett, Systems with Finite Communication Bandwidth Constraints-Ⅰ:State Estimation Problems, IEEE Trans. Auto. Control, Vol.42, No.9,1997, pp.1294-1299.
[17]W. S. Wong, R. and W. Brockett, Systems with Limited Communication Bandwidth Constraints-Ⅱ:Stabilization with Limited Information Feedback, IEEE Trans. Auto. Control, Vol.44, No.5, May 1999, pp.1049-1053.
[18]G. Grassi and S. Mascolo, Nonlinear Observer Design to Synchronize Hyperchaotic Systems via a Scalar Signal, IEEE Circuits and Systems Ⅰ: Fundamental Theory and Application,44, pp.1011-1014,1997.
[19]D. Liberzon, Hybrid Feedback Stabilization of Systems with Quantized Signals, Auto. Control, Vol.39,2003, pp.1543-1554.
[20]D. Liberzon and J. P. Hespanha, Stabilization of Nonlinear Systems with Limited Information Feedback, IEEE, Trans. Auto. Control, Vol.50, No.6, June 2005, pp.910-915.
[21]Qiu Zhanzhi, Zhang Qingling and Zhao Zhiwu, Stability of singular networked-Control systems with control constraint, Journal of Systems Engineering and Electronics, Vol.18, No.2,2007, pp.290-296.
[22]杜昭平,张庆灵,刘丽丽,具有时延及数据包丢失的广义网络化控制系统稳定性分析[J],东北大学学报：自然科学版,2009,30(1)：1005-3026.
[23]Dai L, Singular control systems [M], Berlin:Springer Verlag,1989:5-4
[24]Fuchen Liu, Yu Yao, Fenghua He and Songlin Chen, Stability analysis of networked control systems with time-varying sampling periods[J], Control Theory Appl,2008,6(1):22-25.
[25]Rabello A and Bhaya A, Stability of asynchronous dynamical systems with Rate constrain and application [J], IEEE Proceedings of Control Theory and Application,2002,150(5):546-550.
[26]Hassibi A, Boyd S P and How J P, Control of asynchronous dynamical systems with rate constrains on events[C], Proceedings of the 38th Conference on Decision and Control. Phoenix:IEEE,1999:1345-1351.
[27]Renxin Zhong and Zhi Yang, Roust stability analysis of singular linear systems with delay and parameter uncertainty [J], Control Theory and Application, 2005:195-199.
[28]Zhang W, Branicky M S and Phillips S M, Stability of networked control systems, IEEE Control Systems Magazine,2001,21(1):84-99.
[29]L.A. Montestruque and P. J. Antsaklis, On the Model-based Control of networked systems, Automatic,2003,1837-1843.
[30]G. Walsh, O. Beldiman and L. Bushnell, Error encoding algorithms for network-ed control systems, Automatic,38, pp.261-267,2002.
[31]G. Walsh, O. Beldiman and L. Bushnell, Asymptotic behavior of nonlinear networked control systems, IEEE Trans. Automatic Control,46 (7), pp. 1093-1097,2001.
[32]G. Walsh, H. Ye and L. Bushnell, Stability analysis of networked control systems, IEEE Trans. On Control Systems Technology,10 (3), pp.438-446,2002.
[2]陈关荣,吕金虎,Lorenz系统族的动力学行为,控制与同步,北京,科学出版社,2003.
[3]E. Ott, C. Grebogi and J. A. Yorke, Controlling chaos, Phys. Rev. Lett.,64,1990, pp.1196-1199.
[4]Alexander L. Fradkov, Boris Andrievsky and Robin J. Evans, Chaotic observer-based synchronization under information constraints, Physical Review E 73,066209,2006.
[5]Alexander L. Fradkov, Boris Andrievsky and Robin J. Evans, Adaptive Observer-Based Synchronization of Chaotic Systems with First-Order Coder in the Presence of Information Constraints, IEEE Tran. on Circuits and Systems-Ⅰ Regular Paper, vol.55 (6),2008, pp.1685-1694.
[6]Alexander L. Fradkov, Boris Andrievsky and Robin J. Evans, Controlled synchronization under information constraints, Physical Review E 78,036210, 2008.
[7]Gexia Wang, Zhiming Wang and Guoping Lu, Chaotic synchronization with limited information, Int. J. of Bifurcation and chaos, vol.18 (10),2008, pp.1-9.
[8]A. Savkin, Detectability and output feedback stabilizability of nonlinear networked control systems, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, pp. 8174-8178,2005.
[9]A.L. Fradkov, B. Andrievsky and R. J. Evans, Controlled Synchronization of One Class of Nonlinear Systems under Information Constraints, Math. OC, Dec 2007, pp.1-8.
[10]A.L. Fradkov, B. Andrievsky, Observer-Based Synchronization of Discrete-time Chaotic Systems under Communication Constraints, IFAC, July 2008, pp. 3719-3724.
[11]Hassan K. Khalil, Nonlinear Systems [M],2005:125-130
[12]Guang-Da Hu, Observers for one sided Lipschitz non-Linear systems [J], Journal of Mathematical Control and Information.2006(23):395-401.
[13]Daniel Liberzon and Dragan Nesic, Input-to State Stabilization of Linear Systems with Quantized State Measurements [C], IEEE Trans. Auto. Control, Vol.52, No.5,2007, pp.767-781.
[14]L.Y. Zhao, X. R. Li and G. R. Zhao, Chaotic Synchronization Based on Riccati Inequality with Application to Secure Communication [C], IEEE Trans. Auto. Control, July 2004, pp.1308-1311.
[15]R. W. Brockett and D. Liberzon, Quantized Feedback of Linear Systems, IEEE Trans. Auto. Control, Vol.45, No.7, July 2000, pp.1279-1289:
[16]W. S. Wong and W. Brockett, Systems with Finite Communication Bandwidth Constraints-Ⅰ:State Estimation Problems, IEEE Trans. Auto. Control, Vol.42, No.9,1997, pp.1294-1299.
[17]W. S. Wong, R. and W. Brockett, Systems with Limited Communication Bandwidth Constraints-Ⅱ:Stabilization with Limited Information Feedback, IEEE Trans. Auto. Control, Vol.44, No.5, May 1999, pp.1049-1053.
[18]G. Grassi and S. Mascolo, Nonlinear Observer Design to Synchronize Hyperchaotic Systems via a Scalar Signal, IEEE Circuits and Systems Ⅰ: Fundamental Theory and Application,44, pp.1011-1014,1997.
[19]D. Liberzon, Hybrid Feedback Stabilization of Systems with Quantized Signals, Auto. Control, Vol.39,2003, pp.1543-1554.
[20]D. Liberzon and J. P. Hespanha, Stabilization of Nonlinear Systems with Limited Information Feedback, IEEE, Trans. Auto. Control, Vol.50, No.6, June 2005, pp.910-915.
[21]Qiu Zhanzhi, Zhang Qingling and Zhao Zhiwu, Stability of singular networked-Control systems with control constraint, Journal of Systems Engineering and Electronics, Vol.18, No.2,2007, pp.290-296.
[22]杜昭平,张庆灵,刘丽丽,具有时延及数据包丢失的广义网络化控制系统稳定性分析[J],东北大学学报：自然科学版,2009,30(1)：1005-3026.
[23]Dai L, Singular control systems [M], Berlin:Springer Verlag,1989:5-4
[24]Fuchen Liu, Yu Yao, Fenghua He and Songlin Chen, Stability analysis of networked control systems with time-varying sampling periods[J], Control Theory Appl,2008,6(1):22-25.
[25]Rabello A and Bhaya A, Stability of asynchronous dynamical systems with Rate constrain and application [J], IEEE Proceedings of Control Theory and Application,2002,150(5):546-550.
[26]Hassibi A, Boyd S P and How J P, Control of asynchronous dynamical systems with rate constrains on events[C], Proceedings of the 38th Conference on Decision and Control. Phoenix:IEEE,1999:1345-1351.
[27]Renxin Zhong and Zhi Yang, Roust stability analysis of singular linear systems with delay and parameter uncertainty [J], Control Theory and Application, 2005:195-199.
[28]Zhang W, Branicky M S and Phillips S M, Stability of networked control systems, IEEE Control Systems Magazine,2001,21(1):84-99.
[29]L.A. Montestruque and P. J. Antsaklis, On the Model-based Control of networked systems, Automatic,2003,1837-1843.
[30]G. Walsh, O. Beldiman and L. Bushnell, Error encoding algorithms for network-ed control systems, Automatic,38, pp.261-267,2002.
[31]G. Walsh, O. Beldiman and L. Bushnell, Asymptotic behavior of nonlinear networked control systems, IEEE Trans. Automatic Control,46 (7), pp. 1093-1097,2001.
[32]G. Walsh, H. Ye and L. Bushnell, Stability analysis of networked control systems, IEEE Trans. On Control Systems Technology,10 (3), pp.438-446,2002.