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 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.
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
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)
Article - Journal
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01 Jul 2017