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Zbl 1053.49027
Marigo, Alessia; Piccoli, Benedetto
Regular syntheses and solutions to discontinuous ODEs. (English)
[J] ESAIM, Control Optim. Calc. Var. 7, 291-307 (2002). ISSN 1292-8119; ISSN 1262-3377/e

Summary: 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 Boltyanskij-Brunovsky. We introduce a concept of solution called Krasowskij Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.

MSC 2000:: *49N35 Closed-loop controls
34H05 ODE in connection with control problems
93B50 Synthesis problems
49K15 Optimal control problems with ODE (nec./ suff.)
34A36 Discontinuous equations
93C15 Control systems governed by ODE

Keywords: optimal control; regular synthesis; discontinuous ODEs

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