Journal of Dynamical and Control Systems

, Volume 25, Issue 1, pp 29–43 | Cite as

Necessary First- and Second-Order Optimality Conditions in Discrete Systems with a Delay in Control

  • Misir J. Mardanov
  • Samin T. MalikEmail author


In the paper, an optimal control problem with a delay in control is considered. Suggesting a new approach, Euler-type necessary optimality conditions and the linearized discrete maximum principle are established. Also, the second-order necessary optimality conditions (a) based on the second variation of the objective functional and (b) for quasi-singular controls are obtained. An example to illustrate the richness of content of the suggested approach is presented.


Optimal control Quasi-singular control First and second variations of functional Necessary optimality conditions 

Mathematics Subject Classification (2010)

49J21 49J40 49L20 49M25 49M05 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical and Mechanical Institute of ANASBakuAzerbaijan
  2. 2.Baku Higher Oil SchoolBakuAzerbaijan

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