Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 251340, 10 pages.

Output-Feedback and Inverse Optimal Control of a Class of Stochastic Nonlinear Systems with More General Growth Conditions

Liu Jianwei, Guo Longchuan, Zuo Xin, and Liang Huaqing

Full-text: Open access

Abstract

This paper investigates the problem of output-feedback stabilization for a class of stochastic nonlinear systems in which the nonlinear terms depend on unmeasurable states besides measurable output. We extend linear growth conditions to power growth conditions and reduce the control effort. By using backstepping technique, choosing a high-gain parameter, an output-feedback controller is designed to ensure the closed-loop system to be globally asymptotically stable in probability, and the inverse optimal stabilization in probability is achieved. The efficiency of the output-feedback controller is demonstrated by a simulation example.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 251340, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394806129

Digital Object Identifier
doi:10.1155/2013/251340

Mathematical Reviews number (MathSciNet)
MR3090616

Zentralblatt MATH identifier
06950583

Citation

Jianwei, Liu; Longchuan, Guo; Xin, Zuo; Huaqing, Liang. Output-Feedback and Inverse Optimal Control of a Class of Stochastic Nonlinear Systems with More General Growth Conditions. J. Appl. Math. 2013, Special Issue (2013), Article ID 251340, 10 pages. doi:10.1155/2013/251340. https://projecteuclid.org/euclid.jam/1394806129


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References

  • H. Deng and M. Krstić, “Output-feedback stochastic nonlinear stabilization,” IEEE Transactions on Automatic Control, vol. 44, no. 2, pp. 328–333, 1999.
  • H. Deng and M. Krstić, “Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance,” Systems & Control Letters, vol. 39, no. 3, pp. 173–182, 2000.
  • M. Krstić and H. Deng, Stabilization of Nonlinear Uncertain Systems, Communications and Control Engineering Series, Springer, New York, NY, USA, 1998.
  • Y.-G. Liu and J.-F. Zhang, “Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics,” SIAM Journal on Control and Optimization, vol. 45, no. 3, pp. 885–926, 2006.
  • Z.-J. Wu, X.-J. Xie, and S.-Y. Zhang, “Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function,” International Journal of Control, vol. 79, no. 12, pp. 1635–1646, 2006.
  • S.-J. Liu, J.-F. Zhang, and Z.-P. Jiang, “Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems,” Automatica, vol. 43, no. 2, pp. 238–251, 2007.
  • Z. Pan, Y. Liu, and S. Shi, “Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics,” Science in China. Series F, vol. 44, no. 4, pp. 292–308, 2001.
  • Y. Liu, J. Zhang, and Z. Pan, “Design of satisfaction output feedback controls for stochastic nonlinear systems under quadratic tracking risk-sensitive index,” Science in China. Series F, vol. 46, no. 2, pp. 126–144, 2003.
  • Z.-J. Wu, X.-J. Xie, and S.-Y. Zhang, “Adaptive backstepping controller design using stochastic small-gain theorem,” Automatica, vol. 43, no. 4, pp. 608–620, 2007.
  • X. Yu and X.-J. Xie, “Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics,” IEEE Transactions on Automatic Control, vol. 55, no. 2, pp. 304–320, 2010.
  • W.-Q. Li and X.-J. Xie, “Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable,” Automatica, vol. 45, no. 2, pp. 498–503, 2009.
  • W. Li, X. Liu, and S. Zhang, “Further results on adaptive state-feedback stabilization for stochastic high-order nonlinear systems,” Automatica, vol. 48, no. 8, pp. 1667–1675, 2012.
  • S.-J. Liu and J.-F. Zhang, “Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states,” International Journal of Robust and Nonlinear Control, vol. 18, no. 6, pp. 665–687, 2008.
  • N. Duan and X.-J. Xie, “Further results on output-feedback stabilization for a class of stochastic nonlinear systems,” IEEE Transactions on Automatic Control, vol. 56, no. 5, pp. 1208–1213, 2011.
  • C. Qian, “A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems,” in Proceedings of the American Control Conference (ACC '05), pp. 4708–4715, June 2005.
  • C. Qian and W. Lin, “Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization,” Systems & Control Letters, vol. 42, no. 3, pp. 185–200, 2001.
  • J. Polendo and C. Qian, “A generalized framework for global output feedback stabilization of genuinely nonlinear systems,” in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC '05), pp. 2646–2651, December 2005.
  • X.-J. Xie and W.-Q. Li, “Output-feedback control of a class of high-order stochastic nonlinear systems,” International Journal of Control, vol. 82, no. 9, pp. 1692–1705, 2009.
  • W. Li, Y. Jing, and S. Zhang, “Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable,” Automatica, vol. 46, no. 4, pp. 752–760, 2010.
  • W. Li, X. Liu, and S. Zhang, “Output-feedback stabilization of high-order stochastic nonlinear systems with more general growth conditions,” in Proceedings of the 30th Chinese Control Conference (CCC '11), pp. 5953–5957, July 2011.
  • V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations , vol. 463 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1999.
  • M. Krstić and H. Deng, Stabilization of Uncertain Nonlinear Systems, Springer, New York, NY, USA, 1980.
  • R. Z. Khas'minskii, Stochastic Stability of Differential Equations, vol. 7 of Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics and Analysis, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980.
  • H. Deng and M. Krstić, “Stochastic nonlinear stabilization. II. Inverse optimality,” Systems & Control Letters, vol. 32, no. 3, pp. 151–159, 1997.