Asymptotic expansion of solutions of optimal control problems for discrete weakly controllable systems

Journal of Applied Mathematics and Mechanics

Volumn 66, Issue 2, 2002, Pages 201-213

  Kurina, G A ^a  

^a NONE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036026255     PISSN: 00218928     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8928(02)00025-4     Document Type: Article

References (14)

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3. LYUBUSHIN, A. A., Convergence of the small parameter method for weakly controllable optimal systems. Prikl. Mat. Mekh., 1978, 42, 3, 569-573.
4. PERVOZVANSKII, A. A. and GAITSGORI, V. G., Decomposition, Aggregation and Approximate Optimization. Nauka, Moscow, 1979.
5. CHERNOUS'KO, F. L., AKULENKO, L. D. and SOKOLOV, B. N., The Control of Oscillations. Nauka. Moscow, 1980.
6. POMAZANOV, M. V., The derivation of locally optimal controls of weakly controllable systems from Bellman's equation. Izv. Ross. Akad. Nauk. Teoriya i Sistemy Upravleniya, 1995, 3, 84-93.
7. BELOKOPYTOV, S. V. and DMITRIYEV, M. G., Direct scheme in optimal control problems with fast and slow motions. Systems and Control Letters, 1986, 8, 2, 129-135.
8. BELOKOPYTOV, S. V. and DMITRIYEV, M. G., Solution of classical optimal control problems with a boundary layer. Avtomatika i Telemekhanika, 1989, 7, 71-82.
9. KURINA, G. A., Higher approximations of the small parameter method for weakly controllable systems. Dokl. Ross. Akad. Nauk, 1995, 343, 1, 28-32.
10. GAIPOV, M. A., Asymptotic expansion of the solution of a non-linear discrete optimal control problem with small step-size without restrictions on the control (formalism) I. Izv. Akad. Nauk TSSR, Ser. Fiz.-Tekhn., Khim. i Geol. Nauk, 1990, 1, 9-16.
11. DMITRIYEV, M. G., BELOKOPYTOV, S. V. and GAIPOV, M. A., Asymptotic expansion of the solution of a non-linear discrete optimal control problem with small step-size without restrictions on the control (proofs) II. Izv. Akad. Nauk TSSR, Ser. Fiz.-Tekhn., Khim. i Geol. Nauk, 1990, 2, 10-18.
12. KURINA, G. A., Asymptotic solution of optimal control problems for discrete weakly controllable systems. In Proc. Int. Workshop "New Computer Technologies in Control Systems." Pereslavl-Zallessky, Russia, 1996, pp. 39-40.
13. MOISEYEV, N. N., IVANILOV, Yu. P. and STOLYAPOVA, Ye. M., Optimization Methods. Nauka, Moscow, 1978.
14. VASIL'YEVA, A. B. and DMITRIYEV, M. G., Singular perturbations in optimal control problems. In Advances in Science and Technology. Mathematical Analysis, Vol. 20. VINITI, Moscow, 1982, pp. 3-77.