Nonlinear dynamic systems and optimal control problems on time scales*
College of Science, Guizhou University,
Guiyang, Guizhou 550025, P.R. China. email@example.com; firstname.lastname@example.org;
Revised: 6 December 2009
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.
Mathematics Subject Classification: 37M10 / 35D05 / 49K25 / 90C46
Key words: Time scale / weak solution / optimal control / subdifferentials / existence / necessary conditions of optimality
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