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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. [email protected]; [email protected]; [email protected]
Xiaoling Xiang
Affiliation:
College of Science, Guizhou University, Guiyang, Guizhou 550025, P.R. China. [email protected]; [email protected]; [email protected]
Yang Jiang
Affiliation:
College of Science, Guizhou University, Guiyang, Guizhou 550025, P.R. China. [email protected]; [email protected]; [email protected]
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Abstract

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.

Keywords

Time scaleweak solutionoptimalcontrolsubdifferentialsexistencenecessary conditions ofoptimality
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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