A simple proof of the maximum principle with endpoint constraints

• Autorzy: Korytowski A.
• Języki publikacji: EN

Abstrakty

EN

The paper presents a new, relatively simple proof of Pontryagin’s maximum principle for the canonical problem of optimal control, with equality and inequality constraints imposed on the trajectory endpoints. The proof combines together two ideas, which appeared separately in the earlier works: application of the Karush-John conditions for finite-dimensional problems, and using packages of needle variations.

Słowa kluczowe

EN

optimal control; maximum principle

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2014
• Tom: Vol. 43, no. 1
• Strony: 5--13
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Korytowski A.

• Department of Automatics and Biomedical Engineering AGH University, Krak´ow, Poland

Bibliografia

• 1. DUBOVITSKII, A.YA. and MILYUTIN, A.A. (1965) Extremum problems with restrictions. USSR Comput. Math. and Math. Phys. 5(3), 1-80.
• 2. EDWARDS, R.E. (1995) Functional Analysis: Theory and Applications. Dover Publ., New York.
• 3. MANGASARIAN, L. and FROMOVITZ, S. (1967) The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints. J. Mathematical Analysis and Applications 17, 37-47.
• 4. MILYUTIN, A.A., DMITRUK, A.V. and OSMOLOVSKII, N.P. (2004) Maximum Principle in Optimal Control. Moscow State University, Moscow (in Russian).
• 5. PONTRYAGIN, L.S., BOLTYANSKII, V.G., GAMKRELIDZE, R.V. and MISHCHENKO, E.F. (1961) The Mathematical Theory of Optimal Processes. Nauka, Moscow (in Russian, first English language edition: John Wiley & Sons, Inc., New York, 1962).
• 6. YOSIDA, K. (1965) Functional Analysis. Springer, Berlin.