Geodesic
On the smoothness of an approximated optimization problem for a~Goursat--Darboux system on a~varied domain
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 305-321

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We use an example of a controlled nonlinear Goursat–Darboux system to study a rather general approach to the approximate solution of optimal control problems associated with lumped and distributed parameter systems that are affine in control variables; the domain of independent variables can be fixed or varied. The main idea of this approach consists in the approximation of the original infinite-dimensional optimization problem by a smooth finite-dimensional mathematical programming problem of comparatively small dimension with the help of spline discontinuous interpolation of the desired control on a floating mesh. We establish the existence of partial derivatives for functions of the approximating problem and derive necessary formulas.
Keywords: approximate solving of optimal control problems, Goursat–Darboux system, spline interpolation of the control, floating mesh, derivatives formulas. 
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     author = {A. V. Chernov},
     title = {On the smoothness of an approximated optimization problem for {a~Goursat--Darboux} system on a~varied domain},
     journal = {Trudy Instituta matematiki i mehaniki},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a28/}
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A. V. Chernov. On the smoothness of an approximated optimization problem for a~Goursat--Darboux system on a~varied domain. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 305-321. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a28/