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Nonlinear dynamic systems and optimal control problems on time scales*

Published online by Cambridge University Press:  23 April 2010

Yunfei Peng ,
Xiaoling Xiang  and
Yang Jiang
Yunfei Peng
Affiliation:
College of Science, Guizhou University, Guiyang, Guizhou 550025, P.R. China. pengyf0803@163.com; xxl3621070@yahoo.com.cn; jiangyang415@163.com
Xiaoling Xiang
Affiliation:
College of Science, Guizhou University, Guiyang, Guizhou 550025, P.R. China. pengyf0803@163.com; xxl3621070@yahoo.com.cn; jiangyang415@163.com
Yang Jiang
Affiliation:
College of Science, Guizhou University, Guiyang, Guizhou 550025, P.R. China. pengyf0803@163.com; xxl3621070@yahoo.com.cn; jiangyang415@163.com
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Abstract

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.

Keywords

Time scaleweak solutionoptimal controlsubdifferentialsexistencenecessary conditions of optimality
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 3 , July 2011 , pp. 654 - 681
Copyright
© EDP Sciences, SMAI, 2010

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