Minimum-time optimality of a singular arc: Second order sufficient conditions

Proceedings of the IEEE Conference on Decision and Control

Volumn 1, Issue , 2004, Pages 450-454

  Stefan, Gianna ^a  

^a Dipartimento di Matematica Applicata   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

HAMILTONIANS; INTEGRATION; LINEAR PROGRAMMING; MAXIMUM PRINCIPLE; OPTIMIZATION; RICCATI EQUATIONS; SET THEORY;

BANG-SINGULAR ARC; INPUT AFFINE SYSTEMS; NON-INTERSECTING EXTREMALS; OPTIMALITY;

OPTIMAL CONTROL SYSTEMS;

EID: 14344255957     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. Andrei A. Agrachev and Yu. L. Sachkov. Control Theory from the Geometric View Point. Encyclopaedia of Mathematical Sciences, vol. 87, Springer Verlag 2004.
2. Andrei A. Agrachev, Gianna Stefani, and PierLuigi Zezza. An invariant second variation in optimal control. Internat. J. Control, 71(5):689-715, 1998.
3. Andrei A. Agrachev, Gianna Stefani, and PierLuigi Zezza. Strong minima in optimal control. Proc. Steklov Inst. Math., 220:4-26, 1998. translation from Tr. Mat. Inst. Steklova 220, 8-22, 1998.
4. Andrei A. Agrachev, Gianna Stefani, and PierLuigi Zezza. Strong minima in optimal control. Proc. Steklov Inst. Math., 220:4-26, 1998. translation from Tr. Mat. Inst. Steklova 220, 8-22, 1998.
5. Andrei A. Agrachev, Gianna Stefani, and PierLuigi Zezza. A Hamiltonian approach to strong minima in optimal control. Proc. of Symposia in Pure Mathematics, 64:11-22, 1999.
6. Andrei A. Agrachev, Gianna Stefani, and PierLuigi Zezza. Strong optimality for a bang-bang trajectory. SIAM J. Control Optimization, 41:991-1014, 2002.
7. Vladimir I. Arnold. Mathematical Methods in Classical Mechanics. Springer, New York, 1980.
8. Mariano Giaquinta and Stefan Hildebrandt. Calculus of variations, I and II. Springer, Berlin, 1996.
9. Magnus R. Hestenes. Application of the theory of quadratic forms in Hubert spaces to calculus of variations. Pacific J. Math. 1:521-581, 1951.
10. Magnus R. Hestenes. Calculus of variations and optimal control theory. John Wiley & Sons, New York, New York, 1966.
11. Brian P. Molinari. Non-negativity of a quadratic functional. SIAM J. Control, 13:262-271, 1975.
12. Zsolt Páles and Vera Zeidan Non-smooth optimum problems with constraints. SIAM J. Control Optimization, 32:1476-1502, 1994.
13. Laura Poggiolini and Gianna Stefani. Minimum time optimality of a bang-bang trajectory. In 41st IEEE Conference on Decision and Control, 2002.
14. Laura Poggiolini and Gianna Stefani, State-local optimality of a bang-bang trajectory: a Hamiltonian approach. Systems & Control Letters, in press, 2004.
15. Gianna Stefani and PierLuigi Zezza. Constrained Regular LQControl Problems. SIAM J. Control Optimization, 35:876-900, 1997.
16. Gianna Stefani. On sufficient optimality conditions for a singular extremal. Proceeding of CDC03.
17. Gianna Stefani. Optimality conditions for a singular extremal: the single-input case. Preprint, 2004.
18. Vera Zeidan. The Riccati equation for optimal control problems with mixed state-control constraints: Necessity and sufficiency. SIAM J. Control Optimization , 32:1297-1321, 1994.