Optimal control of a class of nonlocal dispersive equations

Abstract

In this paper, the optimal control problem for a class of nonlocal dispersive equations is considered. We introduce a kind of the definition of a weak solution to this equation and prove the existence of a unique weak solution in a special Hilbert space S(0,T). We also discuss the existence of optimal control solution to a class of nonlocal dispersive equations with the cost functional. Adopting the Dubovitskii–Milyutin functional analytical approach, we prove the necessary optimality condition of optimal control (local maximum principle) for the investigative system in fixed final horizon case.