This paper is mainly
concerned with a class of optimal control problems of systems
governed by the nonlinear dynamic systems on time scales.
Introducing the reasonable weak solution of nonlinear dynamic
systems, the existence of the weak solution for the nonlinear
dynamic systems on time scales and its properties are presented.
Discussing L1-strong-weak lower semicontinuity of integral
functional, we give sufficient conditions for the existence of
optimal controls. Using integration by parts formula and Hamiltonian
function on time scales, the necessary conditions of optimality are
derived respectively. Some examples on continuous optimal control
problems, discrete optimal control problems, mathematical
programming and variational problems are also presented for demonstration.