×

zbMATH — the first resource for mathematics

State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics. (English) Zbl 1127.93354
Summary: For a class of high-order stochastic nonlinear systems with stochastic inverse dynamics which are neither necessarily feedback linearizable nor affine in the control input, this paper investigates the problem of state-feedback stabilization for the first time. Under some weaker assumptions, a smooth state-feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on \([0, \infty)\), the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.

MSC:
93D15 Stabilization of systems by feedback
93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] . Robust Nonlinear Control Design. Birkhauser: Boston, 1995.
[2] Nonlinear Control Systems (3rd edn). Springer: London, 1999. · doi:10.1007/978-1-4471-0549-7
[3] Kokotović, Automatica 37 pp 637– (2001) · Zbl 1153.93301 · doi:10.1016/S0005-1098(01)00002-4
[4] , . Nonlinear and Adaptive Control Design. Wiley: New York, 1995.
[5] . Nonlinear Control Design: Geometric, Adaptive and Robust. Prentice-Hall: Englewood Cliffs, NJ, 1995. · Zbl 0833.93003
[6] , , . Stable Adaptive Control and Estimation for Nonlinear Systems. Wiley: New York, 2002. · doi:10.1002/0471221139
[7] Lin, Systems and Control Letters 39 pp 339– (2000)
[8] Lin, Systems and Control Letters 39 pp 353– (2000)
[9] Lin, IEEE Transactions on Automatic Control 45 pp 1886– (2000)
[10] Lin, IEEE Transactions on Automatic Control 47 pp 1249– (2002)
[11] Lin, IEEE Transactions on Automatic Control 47 pp 1356– (2002)
[12] Lin, IEEE Transactions on Automatic Control 48 pp 1809– (2003)
[13] Qian, IEEE Transactions on Automatic Control 45 pp 1209– (2000)
[14] Qian, Systems and Control Letters 42 pp 185– (2001)
[15] Qian, IEEE Transactions on Automatic Control 46 pp 1061– (2001)
[16] Qian, IEEE Transactions on Automatic Control 47 pp 21– (2002)
[17] Qian, IEEE Transactions on Automatic Control 48 pp 1824– (2003)
[18] Yang, IEEE Transactions on Automatic Control 49 pp 1069– (2004)
[19] Yang, IEEE Transactions on Automatic Control 50 pp 619– (2005)
[20] Stochastic Stability of Differential Equations. Kluwer Academic Publishers: Norwell, MA, 1980. · doi:10.1007/978-94-009-9121-7
[21] Stochastic Stability and Control. Academic Press: New York, 1967.
[22] Pan, IEEE Transactions on Automatic Control 43 pp 1066– (1998)
[23] Pan, SIAM Journal on Control and Optimization 37 pp 957– (1999)
[24] Liu, IEEE Transactions on Automatic Control 48 pp 509– (2003)
[25] Liu, Systems and Control Letters 52 pp 123– (2004)
[26] Liu, Science in China (Series F) 46 pp 126– (2003)
[27] Liu, Science in China (Series F) 47 pp 527– (2004)
[28] Pan, IEEE Transactions on Automatic Control 46 pp 1014– (2001)
[29] Pan, Science in China (Series F) 44 pp 292– (2001)
[30] Deng, Systems and Control Letters 32 pp 143– (1997)
[31] Deng, Systems and Control Letters 32 pp 151– (1997)
[32] Deng, IEEE Transactions on Automatic Control 44 pp 328– (1999)
[33] Deng, Systems and Control Letters 39 pp 173– (2000)
[34] Deng, IEEE Transactions on Automatic Control 46 pp 1237– (2001)
[35] . Stabilization of Uncertain Nonlinear Systems. Springer: New York, 1998. · Zbl 0906.93001
[36] Liu, SIAM Journal on Control and Optimization 45 pp 885– (2006)
[37] Liu, Automatica 43 (2007)
[38] Wu, Automatica 43 (2007)
[39] Wu, International Journal of Control 79 pp 1635– (2006)
[40] . Stochastic Differential Equations. Springer: New York, 1972. · doi:10.1007/978-3-642-88264-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.