Geometry of Jacobi curves. I

Journal of Dynamical and Control Systems

Volumn 8, Issue 1, 2002, Pages 93-140

  Agrachev, A A ^a,b   Zelenko, I ^c  

^a SISSA   (Italy)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Cross ratio; Feedback invariants; Jacobi curve; Lagrange Grassmannian; Symplectic invariants

Indexed keywords

GEOMETRY; MATHEMATICAL TRANSFORMATIONS; THEOREM PROVING; VECTORS;

JACOBI CURVES;

CONTROL SYSTEMS;

EID: 0036381211     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013904801414     Document Type: Article

References (7)

1. A. A. Agrachev and R. V. Gamkrelidze, Feedback-invariant optimal control theory and differential geometry - I. Regular extremals. J. Dynam. Control Systems 3 (1997), No. 3, 343-389.
2. A. A. Agrachev, Feedback-invariant optimal control theory and differential geometry, II. Jacobi curves for singular extremals. J. Dynam. Control Systems 4 (1998), No. 4, 583-604.
3. A. A. Agrachev and I. Zelenko, Principal invariants of Jacobi curves. In: Nonlinear Control in the Year 2000, vol. 1 (A. Isidori, F. Lamnabhi-Lagarrigue and W. Respondek, eds.), Lect. Notes in Control and Inform. Sci. 258 (2001), 9-21.
4. A. A. Agrachev and R. V. Gamkrelidze, Symplectic methods in optimization and control. In: Geometry of Feedback and Optimal Control. (B. Jakubczyk and W. Respondek, eds.), Marcel Dekker, 1997, 1-58.
5. G. Polya and G. Segö, Problems and theorems in analysis I. A series of Comprehensive Studies in Math. Vol. 193, Springer-Verlag, 1978.
6. I. Zelenko, Nonregular abnormal extremals of 2-distribution: Existence, second variation, and rigidity. J. Dynam. Control Systems 5 (1999), No. 3, 347-383.
7. M. I. Zelikin, Homogeneous spaces and Ricatti equation in the calculus of variation. (Russian) Factorial, Moscow, 1998.