Journal of East China Normal University(Natural Sc ›› 2016, Vol. 2016 ›› Issue (1): 19-26.doi: 10.3969/j.issn.1000-5641.2016.01.003

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Contrast structure of higher dimensional singularly perturbed  optimal control problem

 WU  Li-Meng[1] , NI  Ming-Kang[2] , LU  Hai-Bo[3] , ZHANG  Juan[1]   

  • Received:2014-12-29 Online:2016-01-25 Published:2016-03-10

Abstract: In this paper, a class of linear high-dimensional singularly perturbed optimal control problem is discussed. By means of k+\sigma exchange lemma, we prove the existence\linebreak of contrast structure solution for the singularly perturbed optimal control problem. Meanwhile, by virtue of the direct scheme method which is based on boundary function method, we construct the uniformly valid formal asymptotic solution. Finally, an example is presented to illustrate the main results.

Key words: singular perturbation, optimal control, contrast structure

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