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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Existence and Lipschitz regularity of solutions to Bolza problems in optimal control


Authors: P. Cannarsa, H. Frankowska and E. M. Marchini
Journal: Trans. Amer. Math. Soc. 361 (2009), 4491-4517
MSC (2000): Primary 49J15, 49J30, 49K15, 49K30
Published electronically: April 16, 2009
MathSciNet review: 2506416
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Abstract:

In this paper we investigate the existence and Lipschitz continuity of optimal trajectories for the autonomous Bolza problem in control theory. The main feature of our results is that they relax the usual fast growth condition for the Lagrangian. Furthermore, we show that optimal solutions do satisfy the maximum principle.


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Additional Information

P. Cannarsa
Affiliation: Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
Email: cannarsa@axp.mat.uniroma2.it

H. Frankowska
Affiliation: Combinatoire et Optimisation, Université Pierre et Marie Curie (Paris 6) case 189, 4 place Jussieu, 75252 Paris cedex 05, France
Email: frankowska@math.jussieu.fr

E. M. Marchini
Affiliation: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milano, Italy
Email: elsa.marchini@polimi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04765-5
PII: S 0002-9947(09)04765-5
Keywords: Optimal control, Bolza problem, existence of minimizers, Lipschitz optimal trajectory, Lipschitz costate
Received by editor(s): January 27, 2006
Published electronically: April 16, 2009
Additional Notes: This work was supported in part by European Community’s Human Potential Programme under contract HPRN-CT-2002-00281, Evolution Equations. This research was completed in part while the first and third authors visited the CREA, École Polytechnique, Paris and also while the second author visited the Dipartimento di Matematica, Università di Roma “Tor Vergata”
The third author acknowledges the financial support provided through the European Community’s Human Potential Programme under contract HPRN-CT-2002-00281, Evolution Equations.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.