The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control
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Authors
Han Xu
- School of Science, Linyi University, Linyi, Shandong 276005, P. R. China.
Yinlai Jin
- School of Science, Linyi University, Linyi, Shandong 276005, P. R. China.
Abstract
In this article, we discuss a class of three-dimensional non-linear singularly perturbed systems with
optimal control. Firstly, we confirm the existence of heteroclinic orbits connecting two equilibrium points
about their associated systems by necessary conditions of optimal control and functional theory. Secondly,
we study the asymptotic solutions of the singularly perturbed optimal control problems by the methods of
boundary layer functions and prove the existence of the smooth solutions and the uniform validity of the
asymptotic expansion. Finally, we cite an example to illustrate the result.
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ISRP Style
Han Xu, Yinlai Jin, The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2718--2726
AMA Style
Xu Han, Jin Yinlai, The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control. J. Nonlinear Sci. Appl. (2016); 9(5):2718--2726
Chicago/Turabian Style
Xu, Han, Jin, Yinlai. "The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2718--2726
Keywords
- Boundary layer
- Hamilton functions
- heteroclinic orbit
- optimal control.
MSC
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