Global output-feedback finite-time stabilization for a class of stochastic nonlinear cascaded systems

Lan, Qixun ; Niu, Huawei ; Liu, Yamei ; Xu, Huafeng

Kybernetika, Tome 53 (2017) no. 5, pp. 780-802

Abstract (VO)

In this paper, the problem of global finite-time stabilization via output-feedback is investigated for a class of stochastic nonlinear cascaded systems (SNCSs). First, based on the adding a power integrator technique and the homogeneous domination approach, a global output-feedback finite-time control law is constructed for the driving subsystem. Then, based on homogeneous systems theory, it is shown that under some mild conditions the global finite- time stability in probability of the driving subsystem implies the global finite-time stability in probability of the whole SNCS. Finally, a simulation example is given to illustrate the effectiveness of the proposed control design approach.

Détail

DOI : 10.14736/kyb-2017-5-0780

Classification : 39A13, 68M15
Keywords: stochastic nonlinear systems; cascaded systems; output-feedback stabilization; finite-time control

Bibliographie

[1] Chen, Z., Huang, J.: A Lyapunov's direct method for the global robust stabilization of nonlinear cascaded systems. Automatica 44 (2008), 745-752. | DOI | MR

[2] Deng, H., Kristic, M.: Output-feedback stochastic nonlinear stabilization. IEEE Trans. Automat. Control 44 (1999), 328-333. | DOI | MR

[3] Ding, S., Levant, A., Li, S.: Simple homogeneous sliding-mode controller. Automatica 67 (2016), 22-32. | DOI | MR

[4] Ding, S., Li, S., Zheng, W.: Nonsmooth stabilization of a class of nonlinear cascaded systems. Automatica 48 (2012), 2597-2606. | DOI | MR

[5] Ding, S., Wang, J., Zheng, W.: Second-order sliding mode control for nonlinear uncertain systems bounded by positive functions. IEEE Trans. Industrial Electronics 62 (2015), 5899-5909. | DOI

[6] Du, H., He, Y., Cheng, Y.: Finite-time cooperative tracking control for a class of second-order nonlinear multi-agent systems. Kybernetika 49 (2013), 507-523. | MR | Zbl

[7] Du, H., He, Y., Cheng, Y.: Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans. Circ. Syst. 61 (2014), 1778-1788. | DOI

[8] Du, H., Wen, G., Cheng, Y., He, Y., Jia, Ruting: Distributed Finite-Time Cooperative Control of Multiple High-Order Nonholonomic Mobile Robots. IEEE Trans. Neu. Net. Lear. Sys. PP (2016), 99, 1-9. | DOI | MR

[9] Du, H., Wen, G., Yu, X., Li, S., Chen, M.: Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer. Automatica 62 (2015), 236-242. | DOI | MR

[10] Duan, N., Xie, X.: Further results on output-feedback stabilization for a class of stochastic nonlinear systems. IEEE Trans. Automat. Control 56 (2011), 1208-1213. | DOI | MR

[11] Hong, Y., Huang, J., Xu, Y.: On an output feedback finite-time stabilization problem. IEEE Trans. Automat. Control 46 (2001), 305-309. | DOI | MR

[12] Hong, Y., Jiang, Z., Feng, G.: Finite-time input-to-state stability and applications to finite-time control design. SIAM J. Control Optim. 48 (2010), 4395-4418. | DOI | MR | Zbl

[13] Jiang, Z., Mareels, I.: A small-gain control method for nonlinear cascaded systems with dynamic uncertainties. IEEE Trans. Autom. Control 42 (1997), 292-308. | DOI | MR | Zbl

[14] Khoo, S., Yin, J., Man, Z., Yu, X.: Finite-time stabilization of stochastic nonlinear systems in strict-feedback form. Automatica 49 (2013), 1403-1410. | DOI | MR

[15] Lan, Q., Li, S.: Global output-feedback stabilization for a class of stochastic nonlinear systems via sampled-data control. Int. J. Robust Nonlinear Control 27, 17, (2017), 3643-3658. | DOI | MR

[16] Lan, Q., Li, S., Khoo, S., Shi, P.: Global finite-tim stabilisation for a class of stochastic nonlinear systems by output feedback. Int. J. Control 83 (2015), 494-506. | DOI | MR

[17] Lendek, Z., Babuska, R., Schutter, B.: Stability of cascaded fuzzy systems and observers. IEEE Trans. Fuzzy Syst. 17 (2009), 641-653. | DOI

[18] Li, J., Qian, C., Ding, S.: Global finite-time stabilisation by output feedback for a class of uncertain nonlinear systems. Int. J. Control 83 (2010), 2241-2252. | DOI | MR

[19] Li, S., Tian, Y.: Finite-time stability of cascaded time-varying systems. Int. J. Control 80 (2007), 646-657. | DOI | MR | Zbl

[20] Li, W., Xie, X., Zhang, S.: Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions. SIAM J. Control Optim. 49 (2011), 1262-1282. | DOI | MR

[21] Liu, S., Zhang, J.: Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states. Int. J. Robust Nonlinear Control 18 (2008), 665-687. | DOI | MR

[22] Mao, X.: Stochastic Differential Equations and Their Applications. Second edition. Horwood Publishing 1997. | MR

[23] Mazenc, F., Praly, L., Dayawansa, W.: Global stabilization by output feedback: examples and counterexamples. Syst. Control Lett. 23 (1994), 119-125. | DOI | MR

[24] Ou, M., Gu, S., Wang, X., Dong, K.: Finite-Time tracking control of multiple nonholonomic mobile robots with external disturbances. Kybernetika 49 (2013), 1049-1067. | DOI | MR

[25] Rosier, L.: Homogeneous Lyapunov function for homogeneous continuous vector field. Syst. Control Lett. 19 (1992), 467-473. | DOI | MR | Zbl

[26] Sun, H., Hou, L., Zong, G.: Continuous finite time control for static var compensator with mismatched disturbances. Nonlinear Dynamics 85 (2016), 2159-2169. | DOI

[27] Sun, Z., Xue, L., Zhang, K.: A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system. Automatica 58 (2015), 60-66. | DOI | MR

[28] Sun, Z., Yun, M., Li, T.: A new approach to fast global finite-time stabilization of high-order nonlinear terms. Automatica 81 (2017), 455-463. | DOI | MR

[29] Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Automat. Control 46 (2001), 1061-1079. | DOI | MR | Zbl

[30] Qian, C., Lin, W.: Output feedback control for a class of nonlinear systems: a nonseparation principle paradigm. IEEE Trans. Automat. Control 47 (2002), 1710-1715. | DOI | MR

[31] Wu, Y., Gao, F., Liu, Z.: Finite-time state-feedback stabilisation of non-holonomic systems with low-order non-linearities. IET Control Theory Appl. 9 (2015), 1553-1560. | DOI | MR

[32] Wei, Y., Zheng, W.: Finite-time stochastic stabilisation of Markovian jump non-linear quadratic systems with partially known transition probabilities. IET Control Theory Appl. 8 (2014), 311-318. | DOI | MR

[33] Wu, Z., Xie, X., Shi, P., Xia, Y.: Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching. Automatica 45 (2009), 997-1004. | DOI | MR

[34] Wu, Y., Yu, J., Zhao, Y.: Output feedback regulation control for a class of cascaded nonlinear systems and its applications to fan speed control. Nonlinear Anal.: Real World Appl. 13 (2012), 1278-1291. | DOI | MR

[35] Yin, J., Khoo, S.: Conitniuous finite-time state feedback stabilizers for some nonlinear stochastic systems. Int. J. Robust Nonlinear Control 25 (2015), 1581-1600. | DOI | MR

[36] Yin, J., Khoo, S., Man, Z., Yu, X.: Finite-time stability and instability of stochastic nonlinear systems. Automatica 47 (2011), 2671-2677. | DOI | MR | Zbl

[37] Zha, W., Zhai, J., Fei, S., Wang, Y.: Finite-time stabilization for a class of stochastic nonlinear systems via output feedback. ISA Trans. 53 (2014), 709-716. | DOI | MR

[38] Zhou, J., Wen, C., Li, T.: Adaptive output feedback control of uncertain nonlinear systems with hysteresis nonlinearity. IEEE Trans. Automat. Control 57 (2012), 2627-2633. | DOI | MR