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Optimal control for rough differential equations

Laurent Mazliak·Ivan Nourdin
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Abstract

In this note, we consider an optimal control problem associated to a differential equation driven by a Hölder continuous function g of index greater than 1/2. We split our study in two cases. If the coefficient of dg\_t does not depend on the control process, we prove an existence theorem for a slightly generalized control problem, that is we obtain a literal extension of the corresponding deterministic situation. If the coefficient of dg\_t depends on the control process, we also prove an existence theorem but we are here obliged to restrict the set of controls to sufficiently regular functions.

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Laurent Mazliak, Ivan Nourdin. 2006-06-01. Optimal control for rough differential equations. https://arxiv.org/abs/math/0606030

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