International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 297-311
doi:10.1155/S0161171200000880
On the existence of a solution for some distributed optimal control hyperbolic system
Institute of Mathematics, Łódź University, ul. Stefana Banacha 22, Łódź 90-238, Poland
Received 12 December 1994; Revised 30 March 1995
Copyright © 2000 Dariusz Idczak and Stanisław Walczak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.