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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Conjugate points and shocks in
nonlinear optimal control


Authors: N. Caroff and H. Frankowska
Journal: Trans. Amer. Math. Soc. 348 (1996), 3133-3153
MSC (1991): Primary 35B37, 35L67, 49K15, 49L05, 49L20
DOI: https://doi.org/10.1090/S0002-9947-96-01577-2
MathSciNet review: 1344204
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate characteristics of the Hamilton-Jacobi-Bellman
equation arising in nonlinear optimal control and their relationship with weak and strong local minima. This leads to an extension of the Jacobi conjugate points theory to the Bolza control problem. Necessary and sufficient optimality conditions for weak and strong local minima are stated in terms of the existence of a solution to a corresponding matrix Riccati differential equation.


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Additional Information

N. Caroff
Affiliation: CEREMADE, Université Paris-Dauphine, 75775 Paris Cedex 16, France

H. Frankowska
Affiliation: CEREMADE, Université Paris-Dauphine, 75775 Paris Cedex 16, France

DOI: https://doi.org/10.1090/S0002-9947-96-01577-2
Keywords: Hamilton-Jacobi-Bellman equation, characteristics, conjugate point, necessary and sufficient conditions for optimality, Riccati differential equation, shock, value function, weak local minimum
Received by editor(s): November 8, 1993
Received by editor(s) in revised form: May 8, 1995
Article copyright: © Copyright 1996 American Mathematical Society