Contents I. Introduction
High-Order systems are widespread in the real word [1]–[3]. Hence, lots of researchers have focused on high-order nonlinear systems and obtained many significant results.
Abstract:
This paper aims to solve the finite-time stabilization problem for stochastic high-order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured ...Show MoreMetadata
Abstract:
This paper aims to solve the finite-time stabilization problem for stochastic high-order nonlinear systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with finite-time stochastic input-to-state stability (FT-SISS), borrowing from some ideas of the Lyapunov function, sign function, backstepping and FT-SISS methods, and using stochastic finite-time stability theory, a new design and analysis method is given to guarantee global finite-time stability in probability of the closed-loop stochastic systems.
Published in: IEEE Transactions on Automatic Control ( Volume: 64, Issue: 1, January 2019)
Funding Agency:
References is not available for this document.
Select All
1.
C. J. Qian and W. Lin, "A continuous feedback approach to global strong stabilization of nonlinear systems", IEEE Trans. Automat. Control, vol. 46, no. 7, pp. 1061-1079, Aug. 2001.
2.
C. J. Qian and W. Lin, "Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane", IEEE Trans. Automat. Control, vol. 48, no. 10, pp. 1824-1829, Oct. 2003.
3.
X. J. Xie and N. Duan, "Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system", IEEE Trans. Automat. Control, vol. 55, no. 5, pp. 1197-1202, May 2010.
4.
P. Florchinger, A. Iggidr and G. Sallet, "Stochastic processes and their applications", Automatica, vol. 50, no. 2, pp. 235-243, 1994.
5.
H. Deng and M. Krstić, "Stochastic nonlinear stabilization part I: A backstepping design", Syst. Control Lett., vol. 32, pp. 143-150, 1997.
6.
H. Deng and M. Krstić, "Stochastic nonlinear stabilization part II: inverse optimality", Syst. Control Lett., vol. 32, pp. 151-159, 1997.
7.
M. Krstić and H. Deng, Stabilization of Uncertain Nonlinear Systems, New York, NY, USA:Springer, 1998.
8.
H. Deng and M. Krstić, "Output-feedback stochastic nonlinear stabilization", IEEE Trans. Automat. Control, vol. 44, no. 2, pp. 328-333, Feb. 1999.
9.
Z. G. Pan and T. Basar, "Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion", SIAM J. Control Optim., vol. 37, no. 3, pp. 957-995, 1999.
10.
H. Deng and M. Krstić, "Output-feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance", Syst. Control Lett., vol. 39, no. 3, pp. 173-182, 2000.
11.
H. Deng, M. Krstic and R. Williams, "Stabilization of stochastic nonlinear systems driven by noise of unknown covariance", IEEE Trans. Automat. Control, vol. 46, no. 6, pp. 1237-1253, Jun. 2001.
12.
Y. G. Liu, Z. G. Pan and S. J. Shi, "Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost", IEEE Trans. Automat. Control, vol. 48, no. 3, pp. 509-513, Mar. 2003.
13.
J. L. Yin, S. Y. Khoo, Z. H. Man and X. H. Yu, "Finite-time stability and instability of stochastic nonlinear systems", Automatica, vol. 47, no. 12, pp. 2671-2677, 2011.
14.
S. Y. Khoo, J. L. Yin, Z. H. Man and X. H. Yu, "Finite-time stabilization of stochastic nonlinear systems in strict-feedback form", Automatica, vol. 49, no. 5, pp. 1403-1410, 2013.
15.
J. L. Yin and S. Y. Khoo, "Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems", Int. J. Robust Nonlinear Control, vol. 25, no. 11, pp. 1581-1600, 2015.
16.
H. Wang and Q. X. Zhu, "Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form", Automatica, vol. 54, no. 4, pp. 284-291, 2015.
17.
J. Tsinias, "Stochastic ISS and applications to global feedback stabilization", Int. J. Control, vol. 71, no. 5, pp. 907-930, 1998.
18.
C. Tang and T. Basar, "Stochastic stability of singularly perturbed nonlinear systems", Proc. 40th IEEE Conf. Design Control, pp. 399-404, 2001.
19.
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.
20.
S. J. Liu, J. F. Zhang and Z. P. Jiang, "A notion of stochastic input-to-state stability and its application to stability of cascaded stochastic nonlinear systems", Acta Mathematicae Applicatae Sinica, vol. 24, no. 1, pp. 141-156, 2008.
21.
L. Liu and X. J. Xie, "State-feedback stabilization for stochastic high-order nonlinear systems with SISS inverse dynamics", Asian J. Control, vol. 14, no. 1, pp. 207-216, 2012.
22.
L. Liu, S. Yin, H. J. Gao, F. Alsaadi and T. Hayat, "Adaptive partial-state feedback control for stochastic high-order nonlinear systems with stochastic input-to-state stable inverse dynamics", Automatica, vol. 51, no. 1, pp. 285-291, 2015.
23.
P. Zhao, W. Feng, Y. Zhao and Y. Kang, "Finite-time stochastic input-to-state stability of switched stochastic nonlinear systems", Appl. Math. Comput., vol. 268, pp. 1038-1054, 2015.
24.
W. Lin and C. J. Qian, "Adaptive control of nonlinearly parameterized systems: the smooth feedback case", IEEE Trans. Automat. Control, vol. 47, no. 8, pp. 1249-1266, Sep. 2002.
25.
Z. Y. Sun, X. H. Zhang and X. J. Xie, "Continuous global stabilisation of high-order time-delay nonlinear systems", Int. J. Control, vol. 86, no. 6, pp. 994-1007, 2013.
26.
X. Yu and X. J. Xie, "Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics", IEEE Trans. Automat. Control, vol. 55, no. 2, pp. 304-320, Feb. 2010.
27.
X. Yu, X. J. Xie and N. Duan, "Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics", Automatica, vol. 46, no. 11, pp. 1790-1798, 2010.
28.
X. J. Xie, N. Duan and X. Yu, "State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamics", IEEE Trans. Automat. Control, vol. 56, no. 8, pp. 1921-1926, Aug. 2011.
29.
H. Ito and Y. Nishimura, "Stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates", Automatica, vol. 62, no. 1, pp. 51-64, 2015.
30.
H. Ito and Y. Nishimura, "An iISS framework for stochastic robustness of interconnected nonlinear systems", IEEE Trans. Automat. Control, vol. 61, no. 6, pp. 1508-1523, Jun. 2016.
