# Regular syntheses and solutions to discontinuous ODEs

Alessia Marigo; Benedetto Piccoli

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 7, page 291-307
- ISSN: 1292-8119

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topMarigo, Alessia, and Piccoli, Benedetto. "Regular syntheses and solutions to discontinuous ODEs." ESAIM: Control, Optimisation and Calculus of Variations 7 (2002): 291-307. <http://eudml.org/doc/245805>.

@article{Marigo2002,

abstract = {In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii–Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.},

author = {Marigo, Alessia, Piccoli, Benedetto},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal control; regular synthesis; discontinuous ODEs},

language = {eng},

pages = {291-307},

publisher = {EDP-Sciences},

title = {Regular syntheses and solutions to discontinuous ODEs},

url = {http://eudml.org/doc/245805},

volume = {7},

year = {2002},

}

TY - JOUR

AU - Marigo, Alessia

AU - Piccoli, Benedetto

TI - Regular syntheses and solutions to discontinuous ODEs

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 7

SP - 291

EP - 307

AB - In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii–Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.

LA - eng

KW - optimal control; regular synthesis; discontinuous ODEs

UR - http://eudml.org/doc/245805

ER -

## References

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- [13] A. Marigo and B. Piccoli, Safety controls and applications to the dubins’ car. Nonlinear Differential Equations and Applications (in print). Zbl1051.49021
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