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

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.