Applied Mathematics & Optimization

, Volume 79, Issue 1, pp 41–67 | Cite as

Optimal Control Problems for a Semilinear Evolution System with Infinite Delay

  • Fatima Zahra Mokkedem
  • Xianlong FuEmail author


In this paper we study the standard optimal control and time optimal control problems for a class of semilinear evolution systems with infinite delay. We first establish the results of existence and uniqueness of mild solution and the compactness of the solution operator for the control system. Then, based on these results, we investigate the optimal control problem with integral cost function and the time optimal control problem respectively. Under some conditions we show the existence of optimal controls for the both cases of bounded and unbounded admissible control sets. We also obtain the existence of time optimal control to a target set. In addition, a convergence theorem of time optimal controls to a point target set is proved. Finally, an example is given to show the application of the main results.


Evolution system Infinite delay Fundamental solution Optimal control Time optimal control 

Mathematics Subject Classification

34K30 34K35 35R10 93B05 93C10 



This work is supported by NNSF of China (Nos. 11671142 and 11371087), STCSM ( No. 13dz2260400), Shanghai Leading Academic Discipline Project (No. B407).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Laboratoire Système Dynamique et ApplicationsUniversité de Tlemcen (Aboubekr Belkaid University)TlemcenAlgeria
  2. 2.Department of Mathematics, Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghaiPeople’s Republic of China

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