Regular syntheses and solutions to discontinuous ODEs

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 7, Issue , 2002, Pages 291-307

  Marigo, Alessia ^a   Piccoli, Benedetto ^a  

^a CNR   (Italy)

Author keywords

Discontinuous ODEs; Optimal control; Regular synthesis

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FEEDBACK CONTROL; INTEGRAL EQUATIONS; LAGRANGE MULTIPLIERS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS); SET THEORY; VECTORS;

DISCONTINUOUS ORDINARY DIFFERENTIAL EQUATIONS; KRASOWSKI CONE ROBUST SOLUTION; OPTIMAL SYNTHESIS; REGULAR SYNTHESIS; STRATIFIED SOLUTIONS;

CONTROL SYSTEM SYNTHESIS;

EID: 0036409794     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2002013     Document Type: Article

References (18)

1. J.P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag (1984).
2. A. Bicchi, A. Ballucchi, B. Piccoli and P. Soueres, Stability and robustness of optimal synthesis for route tracking by dubins’ vehicles, in Proc. IEEE Int. Conf. on Decision and Control (2000).
3. V.G. Boltyanskii, Sufficient conditions for optimality and the justification of the dynamic programming principle. SIAM J. Control Optim. 4 (1966) 326-361.
4. U. Boscain and B. Piccoli, Extremal synthesis for generic planar systems. J. Dynam. Control Systems 7 (2001) 209-258.
5. A. Bressan and B. Piccoli, A generic classification of time-optimal planar stabilizing feedbacks. SIAM J. Control Optim. 36 (1998) 12-32.
6. P. Brunovsky, Existence of regular syntheses for general problems. J. Differential Equations 38 (1980) 317-343.
7. F.H. Clarke, Y.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic controllability implies feedback stabilization. IEEE Trans. Automat. Control 42 (1997) 1394-1407.
8. A.F. Filippov, Differential Equations with Discontinuous Righthand Sides, Mathematics and Its Applications (Soviet Series). Kluwer Academic Publishers Group (1988). Translated from the Russian.
9. C.G. Gibson, Construction of canonical stratifications, in Topological Stability of Smooth Mappings. Springer Verlag, Berlin, Lecture Notes in Math. 552 (1976) 9-34.
10. M. Goresky and R. MacPherson, Stratified Morse Theory. Springer Verlag, Berlin (1988).
11. A.J. Krener and H. Schättler, The structure of small time reachable sets in low dimensions. SIAM J. Control Optim. 27 (1989) 120-147.
12. J.P. Laumond and P. Souères, Shortest paths synthesis for a car-like robot. IEEE Trans. Automat. Control 41 (1996) 672-688.
13. A. Marigo and B. Piccoli, Safety controls and applications to the dubins’ car. Nonlinear Differential Equations and Applications (in print).
14. A. Marigo and B. Piccoli, Safety driving for the dubins’ car, in XV World Congress on Automatic Control b’02 (in print).
15. R. Murray, Nonlinear control of mechanical systems: A Lagrangian perspective, in IFAC Symposium on Nonlinear Control Systems Design (NOLCOS) (1995) 378-389.
16. B. Piccoli, Classification of generic singularities for the planar time optimal syntheses. SIAM J. Control Optim. 34 (1996) 914-1946.
17. B. Piccoli and H.J. Sussmann, Regular synthesis and sufficiency conditions for optimality. SIAM J. Control Optim. 39 (2000) 359-410.
18. H.J. Sussmann, Regular synthesis for time-optimal control of single-input real analytic systems in the plane. SIAM J. Control Optim. 25 (1987) 1145-1162.