International Journal of Mathematics Trends and Technology
Volume 60 | Number 2 | Year 2018 | Article Id. IJMTT-V60P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P517
In this paper the authors considered optimal control problem involving time delay in the state vector and control vector. Previously some of the authors [1] in their papers considered small delay in optimal control problem. Further literature has been found regarding comparatively large delay [2]. Question arises that how large the delays may be considered so that Pontryagin’s maximum principle may be developed . Here in this paper the authors considered delays in both the state vector and the control vector and find the restriction on the delays to develop Pontryagin’s maximum principle with such delay looking for largest possible.
1. T.E.Aman and D.K.Bhattacharya: Control theoretic Optimization in general delay-di erential equations with small delay. Rev. Acad. Canar. Ciens., XIX (nums1-2), 37-47 (2007).
2. T.E.Aman, A.Ghosh, S.K.Sur and D.K.Bhattacharya: Optimal Control Problem With Comparatively Large Delay.Rev. Acad. Canar. Ciens., XXII (nums1-2), 23-29 (2010).
3. Lee, E.B. and L.Markus: Foundations of optimal control theory. John Willey and sons, Inc. New York (1968).
4. Pontryagin, L.S., V.S.Boltyanski, R. V. Gamkrelidze, and E.F. Ischenko: The mathematical theory of optimal process. Wiley Interscience, New York (1962).
Amit Ghosh, Tanmoy Hazra, Towhid E Aman, "Largest Possible Delay In Control Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 2, pp. 106-109, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P517
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