Reflected dynamics: Viscosity analysis for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">L</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msup></mml:math> cost, relaxation and abstract dynamic programming

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چکیده

We study an optimal control problem consisting in minimizing the L∞ norm of a Borel measurable cost function, finite time, and over all trajectories associated with controlled dynamics which is reflected compact prox-regular set. The first part paper provides viscosity characterization value function for uniformly continuous costs. second concerned linear programming formulations ensued by-products as e.g. dynamic principle merely

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ژورنال

عنوان ژورنال: Journal of Differential Equations

سال: 2021

ISSN: ['1090-2732', '0022-0396']

DOI: https://doi.org/10.1016/j.jde.2021.04.024