Singular extremals in multi-input time-optimal problems: A sufficient condition

Control and Cybernetics

Volumn 39, Issue 4, 2010, Pages 1029-1068

  Chittaro, Francesca C ^a   Stefani, Gianna ^b  

^a UNIV PARIS SUD   (France)

^b Dipartimento di Matematica Applicata   (Italy)

Author keywords

Hamiltonian methods; Second variation; Singular extremal; Sufficient condition

Indexed keywords

EID: 79955369693     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. ABRAHAM, R. and MARSDEN, J. (1978) The Foundation of Mechanics. Addison-Wesley, Reading.
2. AGRACHEV, A.A. and GAMKRELIDZE, R. (1998) Symplectic Methods for Optimization and Control. In: B. Jakubczyk and W. Respondek, eds., Geometry of Feedback and Optimal Control. Marcel Dekker, 1-58.
3. AGRACHEV, A.A. and SACHKOV, Y. (2004) Control Theory from the Geometric Viewpoint. Springer-Verlag, Berlin.
4. AGRACHEV, A.A., STEFANI, G. and ZEZZA, P. (1998a) An invariant second variation in optimal control. Int. J. Control 71 (5), 689-715.
5. AGRACHEV, A.A., STEFANI, G. and ZEZZA, P. (1998b) Strong minima in optimal control. Proc. Stekhlov Inst. Math. 220, 4-26.
6. AGRACHEV, A.A., STEFANI, G. and ZEZZA, P. (2002) Strong Optimality for a Bang-Bang Trajectory. SIAM J. Control and Optimization 41 (4), 991-1014.
7. DMITRUK, A.V. (1977) Quadratic condition for a weak minimum for singular regimes in optimal control problems. Soviet Math. Dokl. 18.
8. DMITRUK, A.V. (1984) Quadratic conditions for a Pontryagin minimum in an optimal control problem linear in the control, with a constraint on the control. Soviet Math. Dokl. 28.
9. DMITRUK, A.V. (2008) Jacobi type conditions for singular extremals. Control and Cybernetics 37 (2), 285-306.
10. GABASOV, R. and KIRILLOVA, F.M. (1972) High order necessary conditions for optimality. SIAM J. Control and Optimization 10, 127-168.
11. GIAQUINTA, M. and HILDEBRANDT, S. (1996) Calculus of Variations - I and II. Springer-Verlag, Berlin.
12. GOH, B.S. (1966) The second variation for singular Bolza problems. SIAM J. Control and Optimization 4, 309-325.
13. HESTENES, M.R. (1951) Application of the theory of quadratic forms in Hubert spaces to the calculus of variations. Pac. J. Math. 1, 525-581.
14. HESTENES, M.R. (1966) Calculus of Variations and Optimal Control. Wiley & Sons, New York.
15. JURDJEVIC, V. (1997) Geometric Control Theory. Cambridge University Press, Cambridge.
16. LEE, J.M. (2006) Introduction to Smooth Manifolds. Springer-Verlag, Berlin.
17. PALES, Z. and ZEIDAN, V. (1994) Non-smooth optimum problems with constraints. SIAM J. Control and Optimization 32, 1476-1502.
18. POGGIOLINI, L. and STEFANI, G. (2004) State-local optimality of a bang-bang trajectory: a Hamiltonian approach. Systems and Control Letters 53, 269-279.
19. POGGIOLINI, L. and STEFANI, G. (2008) Sufficient optimality conditions for a bang-singular extremal in the minimum time problem. Control and Cybernetics 37, 469-490.
20. POGGIOLINI, L. and STEFANI, G. (2009) Sufficient optimality conditions for a bang-singular extremal in the minimum time problem. Submitted to J. Dynamical and Control Systems.
21. STEFANI, G. (2004) Minimum-time optimality of a singular arc: second order sufficient conditions Proc. of CDCO4. IEEE, Control Systems Society.
22. STEFANI, G. (2008) Strong optimality of singular trajectories. In: F. Ancona, A. Bressan, P. Cannarsa, F. Clarke and P. R. Wolenski, eds., Geometry Control and Nonsmooth Analysis.
23. STEFANI, G. and ZEZZA, P. (2002) Constrained regular LQ-control problems. SIAM J. Control and Optimization 35, 3, 876-900.