Abstract
The aim of the paper is to give a high order maximum principle for an optimal control problem in the Mayer form with constraints on the endpoint and to discuss its relations with other analogous results. Only smooth time-independent control systems on ℝn will be considered in order to give a simpler exposition.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. M. Bianchini, G. Stefani, “A high order maximum principle” in “Analysis and control of nonlinear systems”, North-Holland 1988, p. 131–136
R. M. Bianchini, G. Stefani, “Graded approximations and controllability along a trajectory”, SIAM J. Control & Optim. 50 (1990), p. 903–924
R. M. Bianchini, G. Stefani, “Controllability along a trajectory: a variational approach”, preprint.
A. Bressan, “A high order test for optimality of bang-bang controls” SIAM J. Control & Optim. 23 (1985), p. 38–48.
H. Frankowska, “Contingent cones to reachable sets of control systems” SIAM J. Control & Optim. 27 (1989), p. 170–198.
H. Frankowska, “Local controllability of control systems with feedback” J. of Opt. Theory and Appl. 60 (1989), p. 277–296.
H. W. Knobloch, “Higher order necessary conditions in optimal control theory” Lect. Notes in Control and Inf. Sc. 34, Springer Verlag, Berlin 1981.
A. Krener, “The high order maximal principle and its applications to singular extremals” SIAM J. Control & Optim. 15 (1977), p. 256–292.
F. Lamnabhi Lagarrigue, G. Stefani, “Singular optimal problems: on the necessary conditions of optimality” SIAM J, of Control and Opt. 28 (1990), p. 823–840
G. Stefani, “On the local controllability of a scalar-input system” in “Theory and applications of nonlinear control systems”, North Holland 1986, p. 167–179.
H. J. Sussmann, “A general theorem on local controllability”, SIAM J. Control & Optim. 25 (1987), p. 158–194.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Birkhäuser Boston
About this chapter
Cite this chapter
Stefani, G. (1991). On Maximum Principles. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_33
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3214-8_33
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
eBook Packages: Springer Book Archive