Output feedback regulation for large-scale uncertain nonlinear systems with time delays

Liu, Shutang ; Yu, Weiyong ; Zhang, Fangfang

Kybernetika, Tome 51 (2015) no. 5, pp. 874-889

Abstract (VO)

This paper is concerned with the problem of global state regulation by output feedback for large-scale uncertain nonlinear systems with time delays in the states and inputs. The systems are assumed to be bounded by a more general form than a class of feedforward systems satisfying a linear growth condition in the unmeasurable states multiplying by unknown growth rates and continuous functions of the inputs or delayed inputs. Using the dynamic gain scaling technique and choosing the appropriate Lyapunov-Krasovskii functionals, we explicitly construct the universal output feedback controllers such that all the states of the closed-loop system are globally bounded and the states of large-scale uncertain systems converge to zero.

Détail

DOI : 10.14736/kyb-2015-5-0874

Classification : 34K35, 62F35, 93A15, 93B52, 93C10, 93C23
Keywords: global regulation; large-scale systems; output feedback; time-delay systems; uncertain nonlinear systems

Bibliographie

[1] Choi, H.-L., Lim, J.-T.: Stabilisation of non-linear systems with unknown growth rate by adaptive output feedback. Int. J. Systems Sci. 41 (2010), 673-678. | DOI | MR | Zbl

[2] Guan, W.: Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delay. Int. J. Systems Sci. 43 (2012), 682-690. | DOI | MR

[3] Hale, J. K., Lunel, S. M. V.: Introduction to Functional Differential Equations. Springer-Verlag, New York 1993. | DOI | MR | Zbl

[4] Hua, C. C., Wang, Q. G., Guan, X. P.: Memoryless state feedback controller design for time delay systems with matched uncertain nonlinearities. IEEE Trans. Automat. Control 53 (2008), 801-807. | DOI | MR

[5] Jankovic, M.: Control Lyapunov-Razumikhin functions and robust stabilizationof time delay systems. IEEE Trans. Automat. Control 46 (2001), 1048-1060. | DOI | MR

[6] Jiao, X., Shen, T. L.: Adaptive feedback control of nonlinear time-delay systems: The Lasalle-Razumikhinbased Approach. IEEE Trans. Automat. Control 50 (2005), 1909-1913. | DOI | MR

[7] Khalil, H. K., Saberi, A.: Adaptive stabilization of a class of nonlinear systems using high-gain feedback. IEEE Trans. Automat. Control 32 (1987), 1031-1035. | DOI | MR | Zbl

[8] Khalil, H. K.: Nonlinear Systems. Third edition. Prentice Hall, New Jersey 2002.

[9] Koo, M.-S., Choi, H.-L., Lim, J.-T.: Output feedback regulation of a chain of integrators with an unbounded time-varying delay in the input. IEEE Trans. Automat. Control 57 (2012), 2662-2667. | DOI | MR

[10] Krishnamurthy, P., Khorrami, F.: A hign-gain scalling technique for adaptive output feedback control of feedforward systems. IEEE Trans. Automat. Control 49 (2004), 2286-2292. | DOI | MR

[11] Krishnamurthy, P., Khorrami, F.: Feedforward systems with iss appended dynamics: adaptive output-feedback stabilization and disturbance attenuation. IEEE Trans. Automat. Control 53 (2008), 405-412. | DOI | MR

[12] Lei, H., Lin, W.: Universal output feedback control of nonlinear systems with unknown growth rate. Automatica 42 (2006), 1783-1789. | DOI | MR

[13] Lei, H., Lin, W.: Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach. Systems Control Lett. 56 (2007), 529-537. | DOI | MR | Zbl

[14] Mahmoud, M. S.: Decentralized stabilization of interconnected systems with time-varying delays. IEEE Trans. Automat. Control 54 (2009), 2663-2668. | DOI | MR | Zbl

[15] Praly, L., Jiang, Z. P.: Linear output feedback with dynamic hign gain for nonlinear systems. Systems Control Lett. 53 (2004), 107-116. | DOI | MR

[16] Qian, C. J., Lin, W.: Output feedback control of a class of nonlinear systems: a non-separation principle paradigm. IEEE Transaction on Automatic Control 47 (2002), 1710-1715. | DOI | MR

[17] Sepulchre, R., Jankovie, M., V.Kokotovic, P.: Constructive Nonlinear Control. Springer-Verlag, London 1997. | DOI | MR

[18] Shang, F., Liu, Y. G., Zhang, C. H.: Adaptive output feedback stabilization for a class of nonlinear systems with inherent nonlinearities and uncertainties. Int. J. Robust and Nonlinear Control 21 (2011), 157-176. | DOI | MR | Zbl

[19] Tong, S. C., Li, Y. M., Zhang, H. G.: Adaptive Neural Network Decentralized Backstepping Output-Feedback Control for Nonlinear Large-Scale Systems With Time Delays. IEEE Trans. Neural Networks 22 (2011), 1073-1086. | DOI

[20] Wu, H. S.: Decentralised adaptive robust control of uncertain large-scale non-linear dynamical systems with time-varying delays. IET Control Theory and Applications 6 (2012), 629-640. | DOI | MR

[21] Ye, X. D.: Decentralized adaptive stabilization of large-scale nonlinear timedelay systems with unknown high-frequency-gain signs. IEEE Trans. Automat. Control 56 (2011), 1473-1478. | DOI | MR

[22] Zhang, X. F., Gao, H. Y., Zhang, C. H.: Global asymptotic stabilization of feedforward nonlinear systems with a delay in the input. Int. J. Systems Sci. 37 (2006), 141-148. | DOI | MR | Zbl

[23] Zhang, X. F., Baron, L., Liu, Q. G., Boukas, E.-K.: Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems. IEEE Trans. Automat. Control 56 (2011), 692-697. | DOI | MR

[24] Zhang, X. F., Zhang, C. H., Wang, Y. Z.: Decentralized output feedback stabilization for a class of large-scale feedforward nonlinear time-delay systems. Int. J. Robust and Nonlinear Control 24 (2013), 17, 2628-2639. | DOI | MR | Zbl

[25] Zhang, X. F., Liu, L., Feng, G., Zhang, C. H.: Output feedback control of large-scale nonlinear time-delay systems in lower triangular form. Automatica 49 (2013), 3476-3483. | DOI | MR | Zbl

[26] Zhang, X., Lin, Y.: Global adaptive stabilisation of feedforward systems by smooth output feedback. IET Control Theory Appl. 6 (2012), 2134-2141. | DOI | MR