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Stabilizability in optimization problems with unbounded data

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This research is partially supported by the Padua University grant SID 2018 "Controllability, stabilizability and infimun gaps for control systems", prot. BIRD 187147, and by the INdAM-GNAMPA Project 2020 "Extended control problems: gap, higher order conditions and Lyapunov functions"

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  • In this paper we extend the notions of sample and Euler stabilizability to a set of a control system to a wide class of systems with unbounded controls, which includes nonlinear control-polynomial systems. In particular, we allow discontinuous stabilizing feedbacks, which are unbounded approaching the target. As a consequence, sampling trajectories may present a chattering behaviour and Euler solutions have in general an impulsive character. We also associate to the control system a cost and provide sufficient conditions, based on the existence of a special Lyapunov function, which allow for the existence of a stabilizing feedback that keeps the cost of all sampling and Euler solutions starting from the same point below the same value, in a uniform way.

    Mathematics Subject Classification: Primary: 93D05, 93D20; Secondary: 49J15, 49N25.

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