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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 946910, 9 pages
Maximum Principle in the Optimal Control Problems for Systems with Integral Boundary Conditions and Its Extension
1Meshkin Shahr Branch, Islamic Azad University, Meshkin Shahr 5661668691, Iran
2Baku State University, Z. Khalilov Street 23, 1148 Baku, Azerbaijan
3Institute Cybernetics of Azerbaijan National Academy of Sciences, B. Vahab-Zade Street 9, 1141 Baku, Azerbaijan
Received 19 April 2013; Revised 14 June 2013; Accepted 1 July 2013
Academic Editor: Nazim Idrisoglu Mahmudov
Copyright © 2013 A. R. Safari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. Benchohra, J. J. Nieto, and A. Ouahab, “Second-order boundary value problem with integral boundary conditions,” Boundary Value Problems, vol. 2011, Article ID 260309, 9 pages, 2011.
- B. Ahmad and J. J. Nieto, “Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 708576, 11 pages, 2009.
- A. Boucherif, “Second-order boundary value problems with integral boundary conditions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 1, pp. 368–379, 2009.
- R. A. Khan, “Existence and approximation of solutions of nonlinear problems with integral boundary conditions,” Dynamic Systems and Applications, vol. 14, no. 2, pp. 281–296, 2005.
- A. Belarbi, M. Benchohra, and A. Quahab, “Multiple positive solutions for non-linear boundary value problems with integral boundary conditions,” Archivum Mathematicum, vol. 44, no. 1, pp. 1–7, 2008.
- F. P. Vasilev, Optimization Methods, Factorial Press, Moscow, Russia, 2002.
- O. V. Vasiliev, Optimization Methods, vol. 5 of Advanced Series in Mathematical Science and Engineering, World Federation Publishers Company, Atlanta, Ga, USA, 1996.
- A. J. Krener, “The high order maximal principle and its application to singular extremals,” SIAM Journal on Control and Optimization, vol. 15, no. 2, pp. 256–293, 1977.
- H. J. Kelley, R. E. Kopp, and H. G. Moyer, “Singular extremals,” in Topics in Optimization, pp. 63–101, Academic Press, New York, NY, USA, 1967, Edited by G. Leitmann.
- G. Fraser-Andrews, “Finding candidate singular optimal controls: a state of the art survey,” Journal of Optimization Theory and Applications, vol. 60, no. 2, pp. 173–190, 1989.
- R. Gabasov and F. M. Kirillova, Osobye Optimalnye Upravleniya, Nauka, Moscow, Russia, 1973, in Russian.
- K. B. Mansimov, Singular Controls in Systems With Delay, Elm, Baku, Azerbaijan, 1999, in Russian.
- Y. A. Sharifov, “Optimal control of impulsive systems with nonlocal boundary conditions,” Russian Mathematics, no. 2, pp. 75–84, 2013.
- Y. A. Sharifov, “Necessary optimality conditions of first and second order for systems with boundary conditions,” Transactions of National Academy of Sciences of Azerbaijan, vol. 28, no. 1, pp. 189–198, 2008.
- A. Y. Sharifov, “Conditions optimality in problems control with systems impulsive Differential equations under non-local boundary conditions,” Ukrainian Mathematical Journal, vol. 64, no. 6, pp. 836–847, 2012.
- A. Y. Sharifov and N. B. Mammadova, “On second-order necessary optimality conditions in the classical sense for systems with nonlocal conditions,” Differential Equations, vol. 48, no. 4, pp. 605–608, 2012.
- M. F. Mekhtiyev, I. Sh. Djabrailov, and Y. A. Sharifov, “Necessary optimality conditions of second order in classical sense in optimal control problems of three-point conditions,” Journal of Automation and Information Sciences, vol. 42, no. 3, pp. 47–57, 2010.
- O. O. Vasilieva and K. Mizukami, “Optimal control of a boundary value problem,” Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Matematika, no. 12, pp. 33–41, 1994.
- O. O. Vasilieva and K. Mizukami, “Dynamical processes described by a boundary value problem: necessary optimality conditions and solution methods,” Rossiĭskaya Akademiya Nauk. Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, no. 1, pp. 95–100, 2000.
- O. Vasilieva and K. Mizukami, “Optimality criterion for singular controllers: linear boundary conditions,” Journal of Mathematical Analysis and Applications, vol. 213, no. 2, pp. 620–641, 1997.
- O. Vasilieva, “Maximum principle and its extension for bounded control problems with boundary conditions,” International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 35, pp. 1855–1879, 2004.
- Y. A. Sharifov, “Classical necessary optimality conditions in discrete optimal control problems with nonlocal conditions,” Automatic Control and Computer Sciences, vol. 45, no. 4, pp. 192–200, 2011.
- M. F. Mekhtiyev, H. H. Mollai, and Y. A. Sharifov, “On an optimal control problem for nonlinear systems with integral conditions,” Transactions of NAS of Azerbaijan, vol. 25, no. 4, pp. 191–198, 2005.
- A. Ashyralyev and Y. A. Sharifov, “Optimal control problem for impulsive systems with integral boundary conditions,” in AIP Conference Proceedings, vol. 1470, pp. 12–15, 2012.
- A. Ashyralyev and Y. A. Sharifov, “Optimal control problem for impulsive systems with integral boundary conditions,” Electronic Journal of Differential Equations, vol. 2013, no. 80, pp. 1–11, 2013.
- N. N. Samarskii and A. Goolin, Numerical Methods, Nauka, Moscow, Russia, 1989, in Russian.
- H. O. Fattorini, Infinite-Dimensional Optimization and Control Theory, vol. 62, Cambridge University Press, Cambridge, UK, 1999.
- H. O. Fattorini, Infinite Dimensional Linear Control Systems, vol. 201, Elsevier, Amsterdam, The Netherlands, 2005.