Necessary conditions of optimality for a class of optimal control problems on time scales

A class of optimal control problems of a system governed by linear dynamic equations on time scales with quadratic cost functional is considered. By the Lebesgue ΔΔ-integral theory and the Sobolev-type space H1H1 on time scales the weak solution of linear dynamic equations on time scales for both initial value problem and backward problem are introduced, therefore the necessary conditions of optimality are presented. Some typical examples are given for demonstration.