Feedback-invariant optimal control theory and differential geometry - I. Regular extremals

Journal of Dynamical and Control Systems

Volumn 3, Issue 3, 1997, Pages 343-389

  Agrachev, A A ^a   Gamkrelidze, R V ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

Connection; Curvature; Extremal; Geodesic; Hamiltonian

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; INVARIANCE; PROBLEM SOLVING; TENSORS;

CURVATURE TENSOR; DIFFERENTIAL GEOMETRY; LEVI CIVITA CONNECTION; REGULAR EXTREMALS;

OPTIMAL CONTROL SYSTEMS;

EID: 0031191520     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02463256     Document Type: Article

References (17)

1. A. A. Agrachev, Quadratic mappings in geometric control theory. (Russian) Itogi Nauki i Tekhniki VINITI; Problemy Geometrii, Vol. 20, 1988, VINITI, Moscow, 111-205.
2. (English translation: J. Soviet Math., Plenum Publ. Corp., Vol. 51, 1990, 2667-2734).
3. _, Topology of quadratic mappings and Hessians of smooth mappings. (Russian) Itogi Nauki i Tekhniki VINITI; Algebra, Topologia, Geometria, Vol. 26, 1988, VINITI, Moscow, 85-124.
4. (English translation: J. Soviet Math., Plenum Publ. Corp., 1990, 990-1013.)
5. A. A. Agrachev and R. V. Gamkrelidze, Exponential representation of flows and chronological calculus. (Russian) Mat. Sb. 107 (1978), 467-532.
6. (English translation: Math. USSR Sb. 35 (1979), 727-785.)
7. _, The Morse index and the Maslov index for extremals of controlled systems. (Russian) Dokl. Akad. Nauk SSSR 287 (1986), 11-205.
8. (English translation: Soviet Math. Dokl. 33 (1986), 392-395.)
9. _, The extremality index and quasi-extremal controls. (Russian) Dokl. Acad. Nauk SSSR 284 (1985).
10. (English translation: Soviet Math. Dokl. 32 (1985), 478-481.
11. _, The quasi-extremality for controlled systems. (Russian) Itogi Nauki i Tekhniki. VINITI; Sovremennye problemy matematiki. Novejshie dostigeniya, Vol. 35, 1989.
12. (English translation: J. Soviet Math., Plenum Publ. Corp., 1991, 1849-1864.
13. _, Symplectic methods for optimization and control. (to appear in: Geometry of Feedback and Optimal Control, Marcel Dekker.)
14. A. A. Agrachev, R. V. Gamkrelidze, and A. V. Sarychev, Local invariants of smooth control systems. Ado. Appl. Math. 14 (1989), 191-237.
15. V. I. Arnold, Mathematical methods of classical mechanics, Third edition. Nauka, Moscow, 1989.
16. B. Bonnard, Feedback equivalence for nonlinear systems and the time optimal control problems. SIAM J. Control and Optimiz. 29 (1991), 1300-1321.
17. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mischenko, Mathematical theory of optimal processes. Fiz.-mat. giz, Moscow, 1961.