The nonsmooth maximum principle

• Autorzy: Clarke F. H. , Pinho M. R. de
• Języki publikacji: EN

Abstrakty

EN

We present a brief survey of the nonsmooth maximum principle of optimal control, focusing, in particular, upon the alternative forms of the adjoint equation. We obtain a new version of the theorem that asserts for the first time the full Weierstrass condition together with the Euler form of the adjoint equation, thereby extending a result of de Pinho and Vinter. The new theorem also features stratified hypotheses and conclusions. Two examples illustrate its use.

Słowa kluczowe

EN

optimal control; Pontryagin maximum principle; nonsmooth analysis

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2009
• Tom: Vol. 38, no 4A
• Strony: 1151--1167
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Clarke F. H.

autor

Pinho M. R. de

• Universite de Lyon, Institut Camille Jordan, 69622 Villeurbanne, France

Bibliografia

• CLARKE, F. (1973) Necessary Conditions for Nonsmooth Problems in Optimal Control and the Calculus of Variations. PhD thesis, University of Washington.
• CLARKE, F. (1974) Necessary conditions for nonsmooth variational problems. In: Optimal Control Theory and its Applications. Lecture Notes in Econ. and Math. Systems 106. Springer, New York.
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• CLARKE, F. (1975b) Le principe du maximum avec un minimum d’hypothèses. Comptes Rendus Acad. des Sciences de Paris 281, 281-283.
• CLARKE, F. (1976a) The generalized problem of Bolza. SIAM J. Control Optim. 14, 682-699.
• CLARKE, F. (1976b) The maximum principle under minimal hypotheses. SIAM J. Control Optim. 14, 1078-1091.
• CLARKE, F. (2005) Necessary Conditions in Dynamic Optimization. Memoirs Amer. Math. Soc. 816, 178.
• CLARKE, F., LEDYAEV, Yu., STERN, R. and WOLENSKI, P. (1998) Non-smooth Analysis and Control Theory. Springer, New York.
• CLARKE, F. and DE PINHO, M. R. (2009) Optimal control problems with mixed constraints. Preprint.
• DUNFORD, N. and SCHWARTZ, J.T. (1967) Linear Operators Part I. Wiley Interscience, New York.
• IOFFE, A.D. and ROCKAFELLAR, R.T. (1996) The Euler and Weierstrass conditions for nonsmooth variational problems. Calc. Var. Partial Diff. Equations 4, 59-87.
• MILYUTIN, A.A. and OSMOLOVSKII, N.P. (1998) Calculus of Variations and Optimal Control. Trans, of Math. Monographs 160. Amer. Math. Soc., Providence.
• DE PINHO, M.R. and VINTER, R.B. (1995) An Euler-Lagrange inclusion for optimal control problems. IEEE Trans. Automat. Control 40, 1191-1198.
• PONTRYAGIN, L.S., BOLTYANSKII, V.G., GAMKRELIDZE, R.V. and MISCHENKO, E.F. (1962) The Mathematical Theory of Optimal Processes. Wiley-Interscience, New York.
• VINTER, R.B. (2000) Optimal Control. Birkhäuser, Boston.