Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order with Infinite Horizon Planning
AbstractWe establish necessary conditions for the optimality of smooth boundary and initial controls in a semilinear hyperbolic system of the first order. The problem adjoint to the original problem is a semilinear hyperbolic system without initial conditions. The suggested approach is based on the use of special variations of continuously differentiable controls. The existence of global generalized solutions for a semilinear first-order hyperbolic system in a domain unbounded in time is proved. The proof is based on the use of the Banach fixed-point theorem and a space metric with weight functions.
How to Cite
Derev’yanko, N. V., and V. M. Kirilich. “Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order With Infinite Horizon Planning”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 2, Feb. 2015, pp. 185–201, https://umj.imath.kiev.ua/index.php/umj/article/view/1973.