This paper is mainlyconcerned with a class of optimal control problems of systemsgoverned by the nonlinear dynamic systems on time scales.Introducing the reasonable weak solution of nonlinear dynamicsystems, the existence of the weak solution for the nonlineardynamic systems on time scales and its properties are presented.Discussing L1-strong-weak lower semicontinuity of integralfunctional, we give sufficient conditions for the existence ofoptimal controls. Using integration by parts formula and Hamiltonianfunction on time scales, the necessary conditions of optimality arederived respectively. Some examples on continuous optimal controlproblems, discrete optimal control problems, mathematicalprogramming and variational problems are also presented for demonstration.
