Adaptive Output Tracking for Nonlinear Network Control Systems with Time-Delay

Affiliation(s)

College of Automation, Chongqing University of Post and Telecommunications, Chongqing, China.

College of Automation, Chongqing University of Post and Telecommunications, Chongqing, China.

ABSTRACT

The problem of adaptive output tracking is researched for a class of nonlinear network control systems with parameter uncertainties and time-delay. In this paper, a new program is proposed to design a state-feedback controller for this system. For time-delay and parameter uncertainties problems in network control systems, applying the backstepping recursive method, and using Young inequality to process the time-delay term of the systems, a robust adaptive output tracking controller is designed to achieve robust control over a class of nonlinear time-delay network control systems. According to Lyapunov stability theory, Barbalat lemma and Gronwall inequality, it is proved that the designed state feedback controller not only guarantees the state of systems is uniformly bounded, but also ensures the tracking error of the systems converges to a small neighborhood of the origin. Finally, a simulation example for nonlinear network control systems with parameter uncertainties and time-delay is given to illustrate the robust effectiveness of the designed state-feedback controller.

The problem of adaptive output tracking is researched for a class of nonlinear network control systems with parameter uncertainties and time-delay. In this paper, a new program is proposed to design a state-feedback controller for this system. For time-delay and parameter uncertainties problems in network control systems, applying the backstepping recursive method, and using Young inequality to process the time-delay term of the systems, a robust adaptive output tracking controller is designed to achieve robust control over a class of nonlinear time-delay network control systems. According to Lyapunov stability theory, Barbalat lemma and Gronwall inequality, it is proved that the designed state feedback controller not only guarantees the state of systems is uniformly bounded, but also ensures the tracking error of the systems converges to a small neighborhood of the origin. Finally, a simulation example for nonlinear network control systems with parameter uncertainties and time-delay is given to illustrate the robust effectiveness of the designed state-feedback controller.

KEYWORDS

Time-Delay; Network Control Systems; Backstepping Design; Adaptive Control; Output Tracking

Time-Delay; Network Control Systems; Backstepping Design; Adaptive Control; Output Tracking

Cite this paper

J. Yu and H. Zeng, "Adaptive Output Tracking for Nonlinear Network Control Systems with Time-Delay,"*International Journal of Modern Nonlinear Theory and Application*, Vol. 1 No. 3, 2012, pp. 73-80. doi: 10.4236/ijmnta.2012.13010.

J. Yu and H. Zeng, "Adaptive Output Tracking for Nonlinear Network Control Systems with Time-Delay,"

References

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[11] D. Liberzon and J. P. Hespanha, “Stabilization of Nonlinear Systems with Limited Information Feedback,” IEEE Transaction on Automatic Control, Vol. 50, No. 6, 2005, pp. 910-915. doi:10.1109/TAC.2005.849258

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[13] L. Wei and R. Pongvuthithum, “Nonsmooth Adaptive Stabilization of Cascaded Systems with Nonlinear Parameterization via Partial-State Feedback,” IEEE Transaction on Automatic Control, Vol. 48, No. 10, 2003, pp. 1809-1816. doi:10.1109/TAC.2003.817932

[14] Z. Y. Sun and Y. G. Liu, “State-Feedback Adaptive Stabilizing Control Design for a Class of High-Order Nonlinear Systems with Unknown Control Coefficients,” Journal of Systems Science and Complexity, Vol. 20, No. 10, 2007, pp. 350-361. doi:10.1007/s11424-007-9030-5

[15] Z. Y. Sun and Y. G. Liu, “Adaptive Stabilization for a Large Class of High-Order Uncertain Nonlinear Systems,” International Journal of Control, Vol. 82, No. 7, 2009, pp. 1275-1287. doi:10.1080/00207170802549529

[16] Z. Y. Sun, Y. G. Liu and Z. G. Liu, “An Adaptive Controller for a Class of High-Order Nonlinear Systems with Unknown Control Coefficients,” Proceedings of the 30th Chinese Control Conference, Yantai, 22-24 July 2011, pp. 266-271.

[17] N. B. He, C. S. Jiang and Q. Gao, “Adaptive Backstepping Control for a Class of Nonlinear Systems,” 3rd International Conference on Measuring Technology and Mechatronics Automation, Shanghai, 6-7 January 2011, pp. 322-325.

[18] N. B. He, C. S. Jiang and Q. Gao, “Robust Adaptive Backstepping Control of Nonlinear Systems with Uncertainty,” Journal of Applied Sciences Electronics and Information Engineering, Vol. 26, No. 6, 2008, pp. 650-654.

[1] J. P. Hespanha, P. Naghahtabrizi and Y. G. Xu, “A Survey of Recent Results in Networked Control Systems,” Proceedings of the IEEE, Vol. 95, No. 1, 2007, pp. 138-162. doi:10.1109/JPROC.2006.887288

[2] L. A. Montestruque and E. J. Antsaklis, “On the Model-Based Control of Networked Systems,” Automatica, Vol. 39, No. 10, 2003, pp. 1837-1843. doi:10.1016/S0005-1098(03)00186-9

[3] G. C. Walsh, Y. Hong and L. G. Bushnell, “Stability Analysis of Networked Control Systems,” IEEE Transactions on Control Systems Technology, Vol. 10, No. 3, 2002, pp. 438-446. doi:10.1109/87.998034

[4] A. V. Savkin, “Analysis and Synthesis of Networked Control Systems: Topologicall Entropy, Observability, Robustness and Optimal Control,” Automatica, Vol. 41, No. 1, 2006, pp. 51-62. doi:10.1016/j.automatica.2005.08.021

[5] D. Yue, Q. L. Han and C. Peng, “State Feedback Controller Design of Networked Control Systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 51, No. 11, 2004, pp. 640-644. doi:10.1109/TCSII.2004.836043

[6] P. V. Zhivoglyadov and R. H, “Middleton, Networked Control Design for Linear Systems,” Automatica, Vol. 39, No. 4, 2003, pp. 743-750. doi:10.1016/S0005-1098(02)00306-0

[7] T. Yodyium and M. Y. Chow, “Control Methodologies in Networked Control Systems,” Control Engineering Practice, Vol. 11, No. 10, 2003, pp. 1099-1111. doi:10.1016/S0967-0661(03)00036-4

[8] W. Zhang, M. S. Branicky and S. M. Phillips, “Stability of Networked Control Systems,” IEEE Control Systems Magazine, Vol. 21, No. 1, 2001, pp. 84-99. doi:10.1109/37.898794

[9] H. S. Park, Y. H. Kim, D. S. Kim and W. H. Kwon, “A Scheduling Method for Network Based Control Systems,” IEEE Transactions on Control Systems Technology, Vol. 10, No. 3, 2002, pp. 318-330. doi:10.1109/87.998012

[10] D. S. Kim, Y. S. Lee, W. H. Kwon and H. S. Park, “Maximum Allowable Delay Bounds of Networked Control Systems,” Control Engineering Practice, Vol. 11, No. 11, 2003, pp. 1301-1313. doi:10.1016/S0967-0661(02)00238-1

[11] D. Liberzon and J. P. Hespanha, “Stabilization of Nonlinear Systems with Limited Information Feedback,” IEEE Transaction on Automatic Control, Vol. 50, No. 6, 2005, pp. 910-915. doi:10.1109/TAC.2005.849258

[12] D. Yue, Q. Han and J. Lam, “Network-Based Robust Control of Systems with Uncertainty,” Automatica, Vol. 41, No. 6, 2005, pp. 999-1007. doi:10.1016/j.automatica.2004.12.011

[13] L. Wei and R. Pongvuthithum, “Nonsmooth Adaptive Stabilization of Cascaded Systems with Nonlinear Parameterization via Partial-State Feedback,” IEEE Transaction on Automatic Control, Vol. 48, No. 10, 2003, pp. 1809-1816. doi:10.1109/TAC.2003.817932

[14] Z. Y. Sun and Y. G. Liu, “State-Feedback Adaptive Stabilizing Control Design for a Class of High-Order Nonlinear Systems with Unknown Control Coefficients,” Journal of Systems Science and Complexity, Vol. 20, No. 10, 2007, pp. 350-361. doi:10.1007/s11424-007-9030-5

[15] Z. Y. Sun and Y. G. Liu, “Adaptive Stabilization for a Large Class of High-Order Uncertain Nonlinear Systems,” International Journal of Control, Vol. 82, No. 7, 2009, pp. 1275-1287. doi:10.1080/00207170802549529

[16] Z. Y. Sun, Y. G. Liu and Z. G. Liu, “An Adaptive Controller for a Class of High-Order Nonlinear Systems with Unknown Control Coefficients,” Proceedings of the 30th Chinese Control Conference, Yantai, 22-24 July 2011, pp. 266-271.

[17] N. B. He, C. S. Jiang and Q. Gao, “Adaptive Backstepping Control for a Class of Nonlinear Systems,” 3rd International Conference on Measuring Technology and Mechatronics Automation, Shanghai, 6-7 January 2011, pp. 322-325.

[18] N. B. He, C. S. Jiang and Q. Gao, “Robust Adaptive Backstepping Control of Nonlinear Systems with Uncertainty,” Journal of Applied Sciences Electronics and Information Engineering, Vol. 26, No. 6, 2008, pp. 650-654.