Pontryagin's maximum principle for dynamic systems on time scales

In this work, an analogue of Pontryagin's maximum principle for dynamic equations on time scales is given, combining the continuous and the discrete Pontryagin maximum principles and extending them to other cases 'in between'. We generalize known results to the case when a certain set...

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Bibliographic Details
Published inJournal of difference equations and applications Vol. 23; no. 7; pp. 1161 - 1189
Main Authors Bohner, Martin, Kenzhebaev, Kenzhegaly, Lavrova, Olga, Stanzhytskyi, Oleksandr
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.07.2017
Taylor & Francis Ltd
Subjects
34K35
Applied mathematics
Dynamical systems
Lagrange function
Lagrange multiplier
Linear systems
needle-like variations
optimal control
Pontryagin principle
right-dense point
right-scattered point
Time
Time scale
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Summary:In this work, an analogue of Pontryagin's maximum principle for dynamic equations on time scales is given, combining the continuous and the discrete Pontryagin maximum principles and extending them to other cases 'in between'. We generalize known results to the case when a certain set of admissible values of the control is not necessarily closed (but convex) and the attainable set is not necessarily convex. At the same time, we impose an additional condition on the graininess of the time scale. For linear systems, sufficient conditions in the form of the maximum principle are obtained.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2017.1284829