Article
MSC:
62A10,
93C10,
93C15,
93D15,
93D21,
93E12,
93E15 | MR 3245540 | Zbl 1298.93347 | DOI: 10.14736/kyb-2014-3-0450
Full entry |
PDF
(1.2 MB)
Feedback
PDF
(1.2 MB)
Feedback
Keywords:
Barrier Lyapunov Function; output regulation; nonlinear exosystem; Nussbaum gain
Barrier Lyapunov Function; output regulation; nonlinear exosystem; Nussbaum gain
Summary:
This paper studies the constrained robust adaptive stabilization problem for a class of lower triangular systems with unknown control direction. A robust adaptive feedback control law for the systems is proposed by incorporating the technique of Barrier Lyapunov Function with Nussbaum gain. Such a controlled system arises from the study of the constrained robust output regulation problem for a class of output feedback systems with the unknown control direction and a nonlinear exosystem. An application of the constrained robust adaptive stabilization design leads to the solution of the constrained robust output regulation problem in the sense that the output tracking error is constrained within the prescribed barrier limit while asymptotically approaching to zero and the closed loop signals are all bounded for all the time. A numerical example is provided to illustrate the performance of the proposed control.
References:
[1] Čelikovský, S., Huang, J.: Continuous feedback practical output regulation for a class of nonlinear systems having nonstabilizable linearization. In: Proc. IEEE Conference on Decision and Control 1999, Phoenix 1999.
[2] Castillo-Toledo, B., Čelikovský, S., Digennaro, S.: Generalized immersion and nonlinear robust output regulation problem. Kybernetika 40 (2004), 207-220. MR 2069179
[3] Chen, Z., Huang, J.: Global robust servomechanism problem of lower triangular systems in the general case. Systems Control Lett. 52 (2004), 209-220. DOI 10.1016/j.sysconle.2003.10.006 | MR 2062594 | Zbl 1157.93464
[4] Chen, Z., Huang, J.: Dissipativity, stabilization, and regulation of cascade-connected systems. IEEE Trans. Automat. Control 49 (2004), 635-650. DOI 10.1109/TAC.2004.826712 | MR 2057477
[5] Chen, Z., Huang, J.: Robust output regulation with nonlinear exosystems. Automatica 41 (2005), 1447-1454. DOI 10.1016/j.automatica.2005.03.015 | MR 2160490 | Zbl 1086.93013
[6] Chen, H., Sun, W., Sun, Z., Yeow, J. T. W.: Second order sliding mode control of a 2D torsional MEMS micromirror with sidewall electrodes. J. Micromech. Microengrg. 23 (2013), 1-9.
[7] Huang, J.: Nonlinear Output Regulation: Theory and Applications. SIAM, Philadelphia 2004. MR 2308004 | Zbl 1087.93003
[8] Huang, J., Chen, Z.: A general framework for tackling the output regulation problem. IEEE Trans. Automat. Control 49 (2004), 2203-2218. DOI 10.1109/TAC.2004.839236 | MR 2106750
[9] Isidori, A.: Nonlinear Control Systems, Volume II. Springer-Verlag, New York 1999. MR 1410988
[10] Jiang, Z., Mareels, I.: A small-gain control method for nonlinear cascaded systems with dynamic uncertainties. IEEE Trans. Automat. Control 42 (1997), 292-308. DOI 10.1109/9.557574 | MR 1435820 | Zbl 0869.93004
[11] Krstić, M., Kanellakopoulos, I., Kokotović, P.: Nonlinear and Adaptive Control Design. Wiley, New York 1995.
[12] Liu, L., Huang, J.: Global robust stabilization of cascade-connected systems with dynamic uncertainties without knowing the control direction. IEEE Trans. Automat. Control 51 (2006), 1693-1699. DOI 10.1109/TAC.2006.883023 | MR 2262074
[13] Liu, L., Huang, J.: Global robust output regulation of output feedback systems with unknown high-frequency gain sign. IEEE Trans. Automat. Control 51 (2006), 625-631. DOI 10.1109/TAC.2006.872752 | MR 2228023
[14] Marino, R., Tomei, P.: Nonlinear Control Design. Prentice-Hall International, 1995. Zbl 0833.93003
[15] Ma, Y., Islam, S., Pan, Y.: Electrostatic torsional micromirror with enhanced tilting angle using active control methods. IEEE Trans. Mechatronics 16 (2011), 635-650.
[16] Nussbaum, R. D.: Some remaks on a conjecture in parameter adaptive control. Systems Control Lett. 3 (1983), 243-246. MR 0722952
[17] Rehák, B., Čelikovský, S., Ruiz, J., Orozco-Mora, J.: A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem. Kybernetika 45 (2009), 427-444. MR 2543132 | Zbl 1165.93320
[18] Sontag, E. D., Teel, A. R.: Changing supply functions in input/state stable systems. IEEE Trans. Automat. Control 40 (1995), 1476-1478. DOI 10.1109/9.402246 | MR 1343820 | Zbl 0832.93047
[19] Sontag, E. D.: Mathematical control theory. In Texts in Applied Mathematics: Vol. 6. Deterministic finite-dimensional systems (Second edition). Springer-Verlag, New York 1998. MR 1640001
[20] Sun, W., Huang, J., Sun, Z.: Global robust stabilization for a class of time-varying output feedback systems. Internat. J. Robotics and Automation 26 (2011), 93-99. Zbl 1260.93142
[21] Sun, W., Yeow, J. T. W., Sun, Z.: Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking. J. Control Theory Appl. 6 (2012), 111-119. DOI 10.1049/iet-cta.2010.0609 | MR 2919507
[22] Sun, W.: Global robust output regulation of lower triangular systems with nonlinear exosystems and its application. J. Control Theory Appl. 11 (2013), 468-476. DOI 10.1007/s11768-013-2001-6 | MR 3083996
[23] Tee, K. P., Ge, S. S., Tay, E. H.: Barrier Lyapunov Functions for the control of output-constrained nonlinear systems. Automatica 45 (2009), 918-927. DOI 10.1016/j.automatica.2008.11.017 | MR 2535351 | Zbl 1162.93346
[24] Xu, D., Huang, J.: Robust adaptive control of a class of nonlinear systems and its applications. IEEE Trans. Circuits and Systems I: Regular Papers 57 (2010), 691-702. DOI 10.1109/TCSI.2009.2025001 | MR 2729967
[25] Yang, X., Huang, J.: New results on robust output regulation of nonlinear systems with a nonlinear exosystem. Internat. J. Robust and Nonlinear Control 22 (2012), 1703-1719. DOI 10.1002/rnc.1779 | MR 2979770 | Zbl 1274.93076
[26] Ye, X., Jiang, J.: Adaptive nonlinear design without a priori knowledge of control. IEEE Trans. Automat. Control 43 (1998), 1617-1621. DOI 10.1109/9.728882 | MR 1652847 | Zbl 0957.93048
[27] Ye, X.: Decentralized adaptive stabilization of large-scale nonlinear time-delay systems with unknown high-frequency-gain signs. IEEE Trans. Automat. Control 56 (2011), 1473-1478. DOI 10.1109/TAC.2011.2132270 | MR 2839246
[28] Zhang, B., Lan, W.: Improving transient performance for output regulation problem of linear systems with input saturation. Internat. J. Robust and Nonlinear Control 23 (2013), 1087-1098. DOI 10.1002/rnc.2941 | MR 3082138 | Zbl 1286.93081
Search
Partner of
