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May  2019, 24(5): 2293-2313. doi: 10.3934/dcdsb.2019096

## A sufficient optimality condition for delayed state-linear optimal control problems

 Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

*Corresponding author: Delfim F. M. Torres (delfim@ua.pt)

Received  December 2017 Revised  January 2019 Published  March 2019

Fund Project: This work is part of first author's Ph.D., which is carried out at the University of Aveiro

We give answer to an open question by proving a sufficient optimality condition for state-linear optimal control problems with time delays in state and control variables. In the proof of our main result, we transform a delayed state-linear optimal control problem to an equivalent non-delayed problem. This allows us to use a well-known theorem that ensures a sufficient optimality condition for non-delayed state-linear optimal control problems. An example is given in order to illustrate the obtained result.

Citation: Ana P. Lemos-Paião, Cristiana J. Silva, Delfim F. M. Torres. A sufficient optimality condition for delayed state-linear optimal control problems. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2293-2313. doi: 10.3934/dcdsb.2019096
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##### References:
Scheme of new state variables.
Optimal control: green line-initial data; blue line-analytical solution; red dashed line-numerical solution.
Optimal state: green line-initial data; blue line-analytical solution; red dashed line-numerical solution.
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