Powiadomienia systemowe
- Sesja wygasła!
- Sesja wygasła!
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We study nonlinear control systems in the plane, affine with respect to control. We introduce two sets of feedback equivariants forming a phase portrait PP and a parameterized phase portrait PPP of the system. The phase portrait PP consists of an equilibrium set E, a critical set C (parameterized, for PPP), an optimality index, a canonical foliation and a drift direction. We show that under weak generic assumptions the phase portraits determine, locally, the feedback and orbital feedback equivalence class of a system. The basic role is played by the critical set C and the critical vector field on C. We also study local classification problems for systems and their families.
Czasopismo
Rocznik
Tom
Strony
819--847
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw
autor
- Laboratoire de Mathematiques INSA de Rouen Pl. Emile Blondel, 76131 Mont Saint Aignan, France
Bibliografia
- Abed, E.H. and Fu, J.-H. (1986) Local feedback stabilization and bifurcation control, Part I, Hopf bifurcations. Syst. Contr. Lett. 7, 11-17.
- Abed, E.H. and Fu, J.-H. (1987) Local feedback stabilization and bifurcation control, Part *II, Stationary bifurcations. Syst. Contr. Lett. 8, 463-473.
- Baitmann, M. (1978a) Controllability regions on the plane. Diff. Equat. 14, 407-417.
- Baitmann, M. (1978b) Switching lines in the plane. Diff. Equat. 14, 1093-1101.
- Bonnard, B. (1991) Feedback equivalence for nonlinear systems and the time optimal control problem. SIAM J. Control and Optimiz. 29, 1300-1321.
- Boscain, U. and Piccoli, B. (2004) Optimal Synthesis for Control Systems on 2-D Manifolds. SMAI-Springer, Mathematiques et Applications 43.
- Bressan, A. and Piccoli, B. (1998) A generic classification of time optimal planar stabilizing feedbacks. SIAM J. Contr. Optim. 36, 12-32.
- Davydov, A. (1994) Qualitative theory of control systems. Translations of Mathematical Monographs of American Mathematical Society 141.
- Davydov, A. (1998) Controllability of generic systerms on surfaces. In: Jakubczyk, B. and Respondek, W., eds., Geometry of Feedback and Optimal Control. Marcel Dekker, New York, 111-163.
- Hirsch, M. (1976) Differential Topology. Springer, New York.
- Jakubczyk, B. (1998) Critical Hamiltonians and feedback invariants. In: Jakubczyk, B. and Respondek, W., eds., Geometry of Feedback and Optimal Control. Marcel Dekker, New York, 219-256.
- Jakubczyk, B. (2005) Equivalence of deformations of functions germs. In preparation.
- Jakubczyk, B. and Respondek, W. (1990) Feedback equivalence of planar systems and stabilizability. In: M.A. Kaashoek, J.H. van Schuppen and A.C.M. Ran, eds., Robust Control of Linear Systems and Nonlinear Control. Birkhauser, Boston, 447-456.
- Jakubczyk, B. and Respondek, W. (1991) Feedback classification of analytic control systems in the plane, In: B. Bonnard et al., eds., Analysis of Controlled Dynamical Systems. Birkhauser, Boston, 262-273.
- Jakubczyk, B. and Respondek, W. (2005) Bifurcations of 1-parameter families of control-affine systems in the plane. To appear in SIAM J. Contr. Optim.
- Kang, W. (1998) Bifurcation and normal form of nonlinear control systems - part I and part II. SIAM J. Control and Optim. 36, 193-212 and 213-232.
- Krener, A.J., Kang, W. and Chang, D.E. (2004) Control bifurcations. IEEE Trans. Autom. Control 49, 1231-1246.
- Respondek, W. (1998) Feedback classification of nonlinear control systems in R2 and R3. In: Jakubczyk, B. and Respondek, W., eds., Geometry of Feedback and Optimal Control. Marcel Dekker, New York, 347-382.
- Rupniewski, M. (2005) Bifurcations of planar control systems. Submitted.
- Sussmann, H.J. (1987a) The structure of time optimal trajectories for singleinput systems in the plane: the C∞ nonsingular case. SIAM J. Contr. Optim. 25, 433-465.
- Sussmann, H.J. (1987b) The structure of time–optimal trajectories for singleinput systems in the plane: the general real analytic case. SIAM J. Control Opt. 25, 868-904.
- Zhitomirskii, M. (1985) Finitely determined 1-forms ω, wzór are reduced to the models of Darboux and Martinet. Funct. Anal. and its Appl. 19, 71-72.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0008-0016