Largest Possible Delay In Control
Problem

Amit Ghosh; Tanmoy Hazra; Towhid E Aman

doi:https://doi.org/10.14445/22315373/IJMTT-V60P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 60 | Number 2 | Year 2018 | Article Id. IJMTT-V60P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P517

Largest Possible Delay In Control Problem

Amit Ghosh, Tanmoy Hazra, Towhid E Aman

Citation :

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

Abstract

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.

Keywords

Pontryagin’s maximum principle, Delay differential equations, Control Problem, dynamical system.

References

1. T.E.Aman and D.K.Bhattacharya: Control theoretic Optimization in general delay-dierential 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).