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Deterministic minimax impulse control in finite horizon: the viscosity solution approach

Brahim El Asri (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We study here the impulse control minimax problem. We allow the cost functionals and dynamics to be unbounded and hence the value functions can possibly be unbounded. We prove that the value function of the problem is continuous. Moreover, the value function is characterized as the unique viscosity solution of an Isaacs quasi-variational inequality. This problem is in relation with an application in mathematical finance.

Differential flatness and defect: an overview

Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon (1995)

Banach Center Publications

We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems' standpoint, flatness and defect are best defined without...

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