The Maximum Principle for Optimal Control Problems with State Constraints by R.V. Gamkrelidze: Revisited

Journal of Optimization Theory and Applications

Volumn 149, Issue 3, 2011, Pages 474-493

  Arutyunov, A V ^a   Karamzin, D Y ^b,c   Pereira, F L ^c  

^a PEOPLES FRIENDSHIP UNIVERSITY OF RUSSIA   (Russian Federation)

^b DORODNICYN COMPUTING CENTER   (Russian Federation)

^c UNIVERSITY OF PORTO   (Portugal)

Author keywords

Maximum principle; Optimal control; State constraints

Indexed keywords

OPTIMAL CONTROL SYSTEMS;

FIRST-ORDER NECESSARY CONDITIONS; MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL; NON-DEGENERACY; OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROLS; OPTIMAL TRAJECTORIES; REGULARITY ASSUMPTION; STATE CONSTRAINTS;

MAXIMUM PRINCIPLE;

EID: 79955816794     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-011-9807-5     Document Type: Article

References (15)

1. Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., Mishchenko, E. F.: The Mathematical Theory of Optimal Processes. Gordon and Beach, New York (1986).
2. Gamkrelidze, R. V.: Time-optimal process with bounded phase coordinates. Dokl. Akad. Nauk SSSR 125(3), 475-478 (1959).
3. Gamkrelidze, R. V.: Optimal control processes under bounded phase coordinates. Izv. Akad. Nauk SSSR Math. 24(3), 315-356 (1960).
4. Dubovitskii, A. Ya., Milyutin, A. A.: Extremum problems under constraints. Dokl. Akad. Nauk SSSR 149(4), 759-762 (1963).
5. Arutyunov, A. V., Tynyanskii, N. T.: The maximum principle in the problem with state constraints. Izv. Akad. Nauk SSSR. Ser. Tech. Cybern. 4, 60-68 (1984).
6. Arutyunov, A. V.: Optimality Conditions: Abnormal and Degenerate Problems. Math. Appl. Kluwer Academic, Dordrecht (2000).
7. Arutyunov, A. V.: The necessary conditions for optimality the problem with state constraints. Dokl. Akad. Nauk SSSR 280(5), 1033-1037 (1985).
8. Dubovitskii, A. Ya., Dubovitskii, V. A.: Necessary conditions for a strong minimum in optimal control problems with degeneracy of the end-point and phase constraints. Usp. Mat. Nauk 2(2(242)), 175-176 (1985).
9. Arutyunov, A. V.: To the theory of maximum principle in optimal control with state constraints. Dokl. Akad. Nauk SSSR 304(1), 11-14 (1989).
10. Vinter, R.: Optimal Control. Birkhäuser, Boston (2000).
11. Arutyunov, A. V., Chernikova, N. Y.: On the controllability of trajectories in optimal control problems with phase constraints. In: Selected Papers Presented at the International Conference Dedicated to the 90th Anniversary of the Birth of L. S. Pontryagin, Vol. 3, Moscow, Russia, August 31-September 9, 1998. Geometric Control Theory, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., vol. 64, pp. 49-56. VINITI, Moscow (1999).
12. Arutyunov, A. V., Karamzin, D. Yu., Pereira, F. L.: Maximum principle in problems with mixed constraints under weak assumptions of regularity. J. Optim. 59(7), 1067-1083 (2010).
13. Kirillov, A. A., Gvishiani, A. D.: Theorems and Problems of Functional Analysis. Nauka, Moscow (1988) (in Russian).
14. Ioffe, A. D., Tikhomirov, V. M.: Theory of Extremal Problems. North-Holland, Amsterdam (1979).
15. Milyutin, A. A.: Maximum Principle in a General Optimal Control Problem. Fizmatlit, Moscow (2001) (in Russian).