JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ADAPTIVE PARTIAL STABILIZATION, LIMIT DYNAMICS AND BIFURCATION ANALYSIS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ADAPTIVE PARTIAL STABILIZATION, LIMIT DYNAMICS AND BIFURCATION ANALYSIS
Lamooki, Gholam Reza Rokni;
  PDF(new window)
 Abstract
A class of autonomous control systems with fixed unknown parameters is considered to be stabilized with respect to only a part of the variables. A certain type of such systems can be recursively adaptively partially stabilized. The bifurcation analysis reveals the nature of the closed loop system.
 Keywords
partial stability;adaptive control;backstepping;bifurcation;
 Language
English
 Cited by
 References
1.
A. S. Andreyev, Investigation of partial asymptotic stability and instability based on the limiting equations, J. Appl. Math. Mech. 51 (1987), no. 2, 196-201. crossref(new window)

2.
K. J. Astrom and B. Wittenmark, Adaptive Control, Adison-Wesley, 1995.

3.
F. Dumortier and R. Roussarie, Geometric singular perturbation theory beyond normal hyperbolicity, Multiple-time-scale dynamical systems (Minneapolis, MN), 29-63, IMA Vol. Math. Appl., 122, Springer, New York, 2001.

4.
B. Fiedler and S. Liebscher, Takens-Bogdanov bifurcation without parameters and oscillatory shock profiles, Global analysis of dynamical systems, 211-259, Inst. Phys., Bristol, 2001.

5.
J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 2nd edition, 1990.

6.
P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice-Hall, New Jersey, 1996.

7.
M. Krstic, Invariant manifolds and asymptotic properties of adaptive nonlinear stabilizers, IEEE Trans. Automat. Control 41 (1996), no. 6, 817-829. crossref(new window)

8.
M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Adaptive nonlinear control without overparametrization, Systems Control Lett. 19 (1992), no. 3, 177-185. crossref(new window)

9.
M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley & Sons, 1995.

10.
J. A. Leach, S. Triantafillidis, D. H. Owens, and S. B. Townley, The dynamics of universal adaptive stabilization: computational and analytical studies, Control Theory Adv. Tech. 10 (1995), no. 4, 1689-1716.

11.
I. G. Malkin, Theory of Stability of Motion, Izdat. Nauka, Moscow, 2nd edition, 1996.

12.
A. S. Oziraner, On asymptotic stability and instability relative to a part of variables, J. Appl. Math. Mech. 37 (1973), 659-665.

13.
C. Risito, Sulla stabilita asintotica parziale, Ann. Mat. Pura Appl. (4) 84 (1970), 279- 292. crossref(new window)

14.
G. R. Rokni Lamooki and S. B. Townley, Adaptive partial stabilization for non- deterministic strict feedback form, Proc. 11th IEEE Int. Conf. on Meth. and Mod. in Aut. and Robo. MMAR, Poland, (2005), 249-254.

15.
G. R. Rokni Lamooki, S. B. Townley, and H. M. Osinga, Bifurcations and limit dynamics in adaptive control systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15 (2005), no. 5, 1641-1664. crossref(new window)

16.
V. V. Rumyantsev, On the stability of motion with respect to the part of the variables, Vestnik Moscow. Univ. Ser. Mat. Mech Fiz. Astron. Khim. 4 (1957), 9-16.

17.
V. V. Rumyantsev and A. S. Oziraner, The Stability and Stabilization of Motion with Respect to Some of the Variables, Nauka, 1987.

18.
S. B. Townley, An example of a globally stabilizing adaptive controller with a generically destabilizing parameter estimate, IEEE Trans. Automat. Control 44 (1999), no. 11, 2238-2241. crossref(new window)

19.
V. I. Vorotnikov, Partial Stability and Control, Birkhauser, 1998.

20.
V. I. Vorotnikov, Partial stability and control: The state-of-the-art and development prospects, Automation and Remote Control 66 (2005), no. 4, 511-561. crossref(new window)

21.
L. Yang, S. A. Neild, D. J. Wagg, and D. W. Virden, Model reference adaptive control of a nonsmooth dynamical system, Nonlinear Dynamics 46 (2006), no. 3, 323-335. crossref(new window)