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Regular syntheses and solutions to discontinuous ODEs. (English) Zbl 1053.49027
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:
49N35 Optimal feedback synthesis
34H05 Control problems involving ordinary differential equations
93B50 Synthesis problems
49K15 Optimality conditions for problems involving ordinary differential equations
34A36 Discontinuous ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
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