Frank Lempio

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We analyze the Euler discretization to a class of linear-quadratic optimal control problems. First we show convergence of order h for the optimal values, where h is the mesh size. Under the additional assumption that the optimal control has bang-bang structure we show that the discrete and the continuous controls coincide except on a set of measure O(√ h).(More)
Order of convergence results with respect to Hausdorr distance are summarized for the numerical approximation of Au-mann's integral by an extrapolation method which is the set-valued analogue of Romberg's method. This method is applied to the discrete approximation of reachable sets of linear diierential inclusions. For a broad class of linear control(More)
A discrete stability theorem for set-valued Euler's method with state constraints is proven. This theorem is combined with known stability results for differential inclusions with so-called smooth state constraints. As a consequence, order of convergence equal to 1 is proven for set-valued Euler's method, applied to state-constrained differential(More)
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