Approximate Optimal Control for a Nonlinear Hyperbolic Inclusion with Perturbed Nonautonomous Coefficients
摘要
This study addresses an optimal control problem for a nonlinear hyperbolic inclusion with rapidly oscillating nonautonomous coefficients. The main result establishes the convergence of the optimal controls and corresponding trajectories of the original system to those of the averaged problem. The approach is based on the averaging method and compactness arguments, which are employed to justify both the approximation and the existence of optimal pairs for the perturbed system.