Pontryagin's Maximum Principle for Dynamic Systems on Time Scales

Author

Martin Bohner, Missouri University of Science and TechnologyFollow
Kenzhegaly Kenzhebaev
Olga Lavrova
Oleksandr Stanzhytskyi

Abstract

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.

Recommended Citation

M. Bohner et al., "Pontryagin's Maximum Principle for Dynamic Systems on Time Scales," Journal of Difference Equations and Applications, vol. 23, no. 7, pp. 1161 - 1189, Taylor & Francis, Jul 2017.

The definitive version is available at https://doi.org/10.1080/10236198.2017.1284829

Department(s)

Mathematics and Statistics

Keywords and Phrases

Lagrange function; Lagrange multiplier; Needle-like variations; Optimal control; Right-dense point; Right-scattered point; Time scale

International Standard Serial Number (ISSN)

1023-6198; 1563-5120

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Informa UK Limited, trading as Taylor & Francis Group., All rights reserved.

Publication Date

01 Jul 2017