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A class of singularly perturbed optimal control problem is studied by direct scheme method, which is based on the boundary function method. The internal layer solution is proved to be existing, and the uniformly valid asymptotic solution for the singularly perturbed optimal control problem is constructed.
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Keywords:
- asymptotic solution /
- singular perturbation /
- internal layer
[1] Wang C Z, Qin H S 2003 Optimal Control Theory (Beijing: Science Press) (in Chinese) [王朝珠, 秦化淑 2003 最优控制理论 (北京: 科学出版社)]
[2] Tong S G, Wang X X 1995 J. Vib. Shock 14 27 (in Chinese) [童水光, 汪希萱 1995 振动与冲击 14 27]
[3] Zhang H Y, Wang Q 2006 Optimal Control Theory and Application (Beijing: Higher Education Press) (in Chinese) [张洪钺, 王青 2006 最优控制理论与应用 (北京: 高等教育出版社)]
[4] Ni M K, Lin W Z 2009 Asymptotic Theory of Singularly Perturbed Problems (Beijing: Higher Education Press) (in Chinese) [倪明康, 林武忠 2009 奇异摄动问题中的渐近理论 (北京: 高等教育出版社)]
[5] Il'in A M 1991 Maching of Asymptotic Expansions of Solutions of Boundary Value Problem (Providence: American Mthematical Society)
[6] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 60 020202]
[7] Mo J Q 2009 Sci. China G 52 1007
[8] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[9] Mo J Q, Liu S D, Tang R R 2010 Acta Phys. Sin. 59 4403 (in Chinese) [莫嘉琪, 刘树德, 唐荣荣 2010 59 4403]
[10] Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 2910 (in Chinese) [莫嘉琪, 陈贤峰 2010 59 2910]
[11] Mo J Q 2010 Commun. Theor. Phys. 53 440
[12] Mo J Q 2010 Chin. Phys. B 19 010203
[13] Lin W T, Mo J Q, Zhang W J, Chen X F 2008 Acta Phys. Sin. 57 4641 (in Chinese) [林万涛, 莫嘉琪, 张伟江, 陈贤峰 2008 57 4641]
[14] Chen H J, Mo J Q 2010 Acta Phys. Sin. 59 4409 (in Chinese) [陈怀军, 莫嘉琪 2010 59 4409]
[15] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2007 56 6169]
[16] Xie F, Lin Y H, Lin W T, Mo J Q 2011 Acta Phys. Sin. 60 010201 (in Chinese) [谢峰, 林一骅, 林万涛, 莫嘉琪 2011 60 010201]
[17] Wu Q K 2011 Acta Phys. Sin. 60 068802 (in Chinese) [吴钦宽 2011 60 068802]
[18] Fridman E, Shaked U 2000 Automatica 36 1181
[19] Liu H P, Sun F C, Hu Y N 2005 Fuzzy Set. Syst. 155 272
[20] Subbotina N N 2007 Math. Comput. Model. 45 1284
[21] Koskie S, Coumarbatch C, Gajic Z 2010 Appl. Math. Comput. 216 1401
[22] Lee C B, Li R Q 2006 J. Hydrodyn. B 18 26
[23] Lin X B 1989 SIAM J. Appl. Math. 49 26
[24] Belokopytov S V, Dmitriev M G 1989 Avtom. Telemekh. 7 71
[25] Ni M K, Dmitriev M G 1998 Avtom. Telemekh. 5 41
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[1] Wang C Z, Qin H S 2003 Optimal Control Theory (Beijing: Science Press) (in Chinese) [王朝珠, 秦化淑 2003 最优控制理论 (北京: 科学出版社)]
[2] Tong S G, Wang X X 1995 J. Vib. Shock 14 27 (in Chinese) [童水光, 汪希萱 1995 振动与冲击 14 27]
[3] Zhang H Y, Wang Q 2006 Optimal Control Theory and Application (Beijing: Higher Education Press) (in Chinese) [张洪钺, 王青 2006 最优控制理论与应用 (北京: 高等教育出版社)]
[4] Ni M K, Lin W Z 2009 Asymptotic Theory of Singularly Perturbed Problems (Beijing: Higher Education Press) (in Chinese) [倪明康, 林武忠 2009 奇异摄动问题中的渐近理论 (北京: 高等教育出版社)]
[5] Il'in A M 1991 Maching of Asymptotic Expansions of Solutions of Boundary Value Problem (Providence: American Mthematical Society)
[6] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 60 020202]
[7] Mo J Q 2009 Sci. China G 52 1007
[8] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[9] Mo J Q, Liu S D, Tang R R 2010 Acta Phys. Sin. 59 4403 (in Chinese) [莫嘉琪, 刘树德, 唐荣荣 2010 59 4403]
[10] Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 2910 (in Chinese) [莫嘉琪, 陈贤峰 2010 59 2910]
[11] Mo J Q 2010 Commun. Theor. Phys. 53 440
[12] Mo J Q 2010 Chin. Phys. B 19 010203
[13] Lin W T, Mo J Q, Zhang W J, Chen X F 2008 Acta Phys. Sin. 57 4641 (in Chinese) [林万涛, 莫嘉琪, 张伟江, 陈贤峰 2008 57 4641]
[14] Chen H J, Mo J Q 2010 Acta Phys. Sin. 59 4409 (in Chinese) [陈怀军, 莫嘉琪 2010 59 4409]
[15] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪, 张伟江, 陈贤峰 2007 56 6169]
[16] Xie F, Lin Y H, Lin W T, Mo J Q 2011 Acta Phys. Sin. 60 010201 (in Chinese) [谢峰, 林一骅, 林万涛, 莫嘉琪 2011 60 010201]
[17] Wu Q K 2011 Acta Phys. Sin. 60 068802 (in Chinese) [吴钦宽 2011 60 068802]
[18] Fridman E, Shaked U 2000 Automatica 36 1181
[19] Liu H P, Sun F C, Hu Y N 2005 Fuzzy Set. Syst. 155 272
[20] Subbotina N N 2007 Math. Comput. Model. 45 1284
[21] Koskie S, Coumarbatch C, Gajic Z 2010 Appl. Math. Comput. 216 1401
[22] Lee C B, Li R Q 2006 J. Hydrodyn. B 18 26
[23] Lin X B 1989 SIAM J. Appl. Math. 49 26
[24] Belokopytov S V, Dmitriev M G 1989 Avtom. Telemekh. 7 71
[25] Ni M K, Dmitriev M G 1998 Avtom. Telemekh. 5 41
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