Optimization of a Fractional Differential Equation
We consider a linear quadratic optimization problem where the state is governed by a fractional ordinary differential equation. We also consider control constraints. We show existence and uniqueness of an optimal state–control pair and propose a method to approximate it. Due to the low regularity of the solution to the state equation, rates of convergence cannot be proved unless problematic assumptions are made. Instead, we appeal to the theory of Γ-convergence to show the convergence of our scheme.
E. Otárola was supported in part by CONICYT through FONDECYT project 3160201. A.J. Salgado was supported in part by NSF grant DMS-1418784.
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