A simple proof of the maximum principle with endpoint constraints

• Autorzy: Adam Korytowski
• 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. (original abstract)

Słowa kluczowe

PL

Teoria optymalizacji; Teoria kontroli

EN

Optimization theory; Control theory

• Czasopismo: Control and Cybernetics
• Rocznik: 2014
• Tom: 43
• Numer: nr 1
• Strony: 5-13

Twórcy

autor

Adam Korytowski

• AGH University of Science and Technology Kraków, Poland

Bibliografia

• Dubovitskii, A.Ya; Milyutin, A.A. (1965) Extremum problems with restrictions. USSR Comput. Math. and Math. Phys. 5(3), 1-80.
• Edwards, R.E. (1995) Functional Analysis: Theory and Applications. Dover Publ., New York.
• Mangasarian, L.; 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.
• Milyutin, A.A.; Dmitruk, A.V.; Osmolovskii, N.P. (2004) Maximum Principle in Optimal Control. Moscow State University, Moscow (in Russian).
• Pontryagin, L.S.; Boltyanskii, V.G.; Gamkrelidze, R.V.; 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).
• Yosida, K. (1965) Functional Analysis. Springer, Berlin.