Nonlinear integro‐differential equations and optimal control problems on time scales

This paper is mainly concerned with a class of optimal control problems of a system governed by the nonlinear integro‐differential equation on time scales. Using the contraction mapping principle, the existence and uniqueness of a weak solution of the nonlinear integro‐differential equation on time scales are proved. Discussing $L_{‐{T}}^1$ ‐strong–weak lower semicontinuity of integral functional on time scales, we give sufficient conditions for the existence of optimal control. By the virtue of the integration by parts formula on time scales, the necessary conditions of optimality are derived.