Abstract and Applied Analysis

Resilient Finite-Time Controller Design of a Class of Stochastic Nonlinear Systems

Zhiguo Yan

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Abstract

This paper deals with the problem of resilient finite-time control for a class of stochastic nonlinear systems. The notion of finite-time annular domain stability of stochastic nonlinear systems is first introduced. Then, some sufficient conditions are given for the existence of resilient state feedback finite-time annular domain stabilizing controller, which are expressed in terms of matrix inequalities. A double-parameter searching algorithm is proposed to solve these obtained matrix inequalities. Finally, an example is given to illustrate the effectiveness of the developed method.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 791409, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412278126

Digital Object Identifier
doi:10.1155/2014/791409

Mathematical Reviews number (MathSciNet)
MR3224321

Zentralblatt MATH identifier
07023075

Citation

Yan, Zhiguo. Resilient Finite-Time Controller Design of a Class of Stochastic Nonlinear Systems. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 791409, 9 pages. doi:10.1155/2014/791409. https://projecteuclid.org/euclid.aaa/1412278126


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References

  • F. Amato, M. Ariola, and P. Dorato, “Finite-time control of linear systems subject to parametric uncertainties and disturbances,” Automatica, vol. 37, no. 9, pp. 1459–1463, 2001.
  • F. Amato, M. Ariola, and C. Cosentino, “Finite-time stabilization via dynamic output feedback,” Automatica, vol. 42, no. 2, pp. 337–342, 2006.
  • W. Zhang and X. An, “Finite-time control of linear stochastic systems,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 3, pp. 687–694, 2008.
  • F. Amato, M. Ariola, and C. Cosentino, “Finite-time stability of linear time-varying systems: analysis and controller design,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 1003–1008, 2010.
  • Y. Yang, J. Li, and G. Chen, “Finite-time stability and stabilization of nonlinear stochastic hybrid systems,” Journal of Mathematical Analysis and Applications, vol. 356, no. 1, pp. 338–345, 2009.
  • Z. Yan, G. Zhang, and J. Wang, “Non-fragile robust finite-time ${H}_{\infty }$ control for nonlinear stochastic Itô systems using neural network,” International Journal of Control, Automation and Systems, vol. 10, no. 5, pp. 873–882, 2012.
  • Z. Yan and G. Zhang, “Finite-time ${H}_{\infty }$ filtering for a class of nonlinear stochastic uncertain systems,” Control and Decision, vol. 29, no. 3, pp. 419–424, 2012.
  • Z. Yan, G. Zhang, and W. Zhang, “Finite-time stability and stabilization of linear Itô stochastic systems with state and control-dependent noise,” Asian Journal of Control, vol. 15, no. 1, pp. 270–281, 2013.
  • J. Ge and Y. Xu, Internal Medicine, People's Press, 2013 (Chinese).
  • W. Zhang and B. S. Chen, “State feedback ${H}_{\infty }$ control for a class of nonlinear stochastic systems,” SIAM Journal on Control and Optimization, vol. 44, no. 6, pp. 1973–1991, 2006.
  • W. Zhang, H. Zhang, and B.-S. Chen, “Stochastic ${H}_{2}/{H}_{\infty }$ control with $(x,u,{\lightv})$-dependent noise: finite horizon case,” Automatica, vol. 42, no. 11, pp. 1891–1898, 2006.
  • W. Zhang and G. Feng, “Nonlinear stochastic ${H}_{2}/{H}_{\infty }$ control with $(x,u,{\lightv})$-dependent noise: infinite horizon case,” IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1323–1328, 2008.
  • Z. Lin, J. Liu, Y. Lin, and W. Zhang, “Nonlinear stochastic passivity, feedback equivalence and global stabilization,” International Journal of Robust and Nonlinear Control, vol. 22, no. 9, pp. 999–1018, 2012.
  • G. H. Yang and W. W. Che, “Non-fragile ${H}_{\infty }$ filter design for linear continuous-time systems,” Automatica, vol. 44, no. 11, pp. 2849–2856, 2008.
  • X. G. Guo and G. H. Yang, “Non-fragile ${H}_{\infty }$ filter design for delta operator formulated systems with circular region pole constraints: an LMI optimization approach,” Acta Automatica Sinica, vol. 35, no. 9, pp. 1209–1215, 2009.
  • X. Mao, Stochastic Differential Equations and Applications, Horwood Publishing, Chichester, UK, 2nd edition, 2008.
  • S. Battilotti and A. De Santis, “Stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set,” IEEE Transactions on Automatic Control, vol. 48, no. 9, pp. 1585–1599, 2003.
  • H. Mukaidani, “The guaranteed cost control for uncertain nonlinear large-scale stochastic systems via state and static output feedback,” Journal of Mathematical Analysis and Applications, vol. 359, no. 2, pp. 527–535, 2009.
  • I. R. Petersen, “Robust output feedback guaranteed cost control of nonlinear stochastic uncertain systems via an IQC approach,” IEEE Transactions on Automatic Control, vol. 54, no. 6, pp. 1299–1304, 2009.
  • Z. Yan, G. Zhang, and J. Wang, “Non-fragile robust finite-time stabilization for nonlinear stochastic systems via neural network,” in Proceedings of the 8th Asian Control Conference (ASCC '11), pp. 547–552, Kaohsiung, Taiwan, May 2011.
  • S. Limanond and J. Si, “Neural-network-based control design: an LMI approach,” IEEE Transactions on Neural Networks, vol. 9, no. 6, pp. 1422–1429, 1998.
  • C. L. Lin and T. Y. Lin, “An ${H}_{\infty }$ design approach for neural net-based control schemes,” IEEE Transactions on Automatic Control, vol. 46, no. 10, pp. 1599–1605, 2001.
  • X. Luan, F. Liu, and P. Shi, “Robust finite-time ${H}_{\infty }$ control for nonlinear jump systems via neural networks,” Circuits, Systems, and Signal Processing, vol. 29, no. 3, pp. 481–498, 2010.
  • H. Zhang, Y. Shi, and A. S. Mehr, “Robust ${H}_{\infty }$ PID control for multivariable networked control systems with disturbance/noise attenuation,” International Journal of Robust and Nonlinear Control, vol. 22, no. 2, pp. 183–204, 2012.
  • H. Zhang, J. M. Wang, and Y. Shi, “Robust ${H}_{\infty }$ sliding-mode control for Markovian jump systems subject to intermittent observations and partially known transition probabilities,” Systems and Control Letters, vol. 62, no. 12, pp. 1114–1124, 2013.
  • H. Zhang, Y. Shi, and J. M. Wang, “Observer-based tracking controller design for networked predictive control systems with uncertain Markov delays,” International Journal of Control, vol. 86, no. 10, pp. 1824–1836, 2013.
  • H. Zhang, Y. Shi, and J. M. Wang, “On energy-to-peak filtering for non-uniformly sampled nonlinear systems: a Markovian jump system approach,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 212–222, 2014. \endinput