Dariusz Idczak, Stanislaw Walczak, "On the existence of a solution for some distributed optimal control hyperbolic system", International Journal of Mathematics and Mathematical Sciences, vol. 23, Article ID 169637, 15 pages, 2000. https://doi.org/10.1155/S0161171200000880
On the existence of a solution for some distributed optimal control hyperbolic system
We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. We prove a theorem on the existence of an optimal process in the classes of absolutely continuous trajectories of two variables and measurable controls with values in a fixed compact and convex set.
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