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

Ana P. Lemos-Paião; Cristiana J. Silva; Delfim F. M. Torres

doi:10.3934/dcdsb.2019096

Article Contents

2019, Volume 24, Issue 5: 2293-2313. Doi: 10.3934/dcdsb.2019096 open access

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

Received: November 30, 2017

Revised: December 31, 2018

Early access: March 2019

Published: March 2019

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 49K15; Secondary: 34H99.

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Figure 1. Scheme of new state variables.

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Figure 2. Optimal control: green line-initial data; blue line-analytical solution; red dashed line-numerical solution.

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Figure 3. Optimal state: green line-initial data; blue line-analytical solution; red dashed line-numerical solution.

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