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January  2009, 5(1): 1-10. doi: 10.3934/jimo.2009.5.1

A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales

Y. Gong 1, and  X. Xiang 1,

1. 

Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, China

Received  February 2008 Revised  August 2008 Published  December 2008

This paper is mainly concerned with a class of optimal control problems of systems governed by the first order linear dynamic equations on time scales with quadratic cost functionals. Introducing the weak solutions of the first order linear dynamic equations and presenting the Arzela-Ascoli theorem on time scales, we prove the existence of solution to a class of linear quadratic optimal control problems on time scales.
Keywords: Banach space, optimal control., Arzela-Ascoli theorem, time scales, $\Delta$-derivative, dynamic equations.
Mathematics Subject Classification: 39A1.
Citation: Y. Gong, X. Xiang. A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales. Journal of Industrial and Management Optimization, 2009, 5 (1) : 1-10. doi: 10.3934/jimo.2009.5.1
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