Abstract
The first order sensitivity analysis is performed for a class of optimal control problems for time lag parabolic equations in which retarded arguments appear in the integral form with h ∈ (0, b) in the state equations and with k ∈ (0, c) in the Neumann boundary conditions. The optimality system is analyzed with the respect to a small parameter. The directional derivative of the optimal control is obtained as a solution to an auxiliary optimization problem. The control constraints for the auxilary optimization problem are received.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
1. Emirsajłow, Z., Kowalewski, A., Krakowiak, A., Sokołowski, J.: Sensitivity analysis of parabolic optimal control problems. Proceedings of the 10th IEEE International Conference on Methods and Models in Automation and Robotics 1, 37–42 (29 August - 1 September 2005, Miȩdzyzdroje, Poland)
2. Emirsajłow, Z., Kowalewski, A., Krakowiak, A., Sokołowski, J.: Sensitivity analysis of time delays parabolic optimal control problems. Proceedings of the 12th IEEE International Conference on Methods and Models in Automation and Robotics 1, 105–109 (28-31 August 2006, Miȩdzyzdroje, Poland)
3. Kowalewski, A., Emirsajłow, Z. Sokołowski, J., Krakowiak, A.: Sensitivity of optimal controls for time delay parabolic systems. Proceedings of the 21 IEEE International Conference on Methods and Models in Automation and Robotics, 511–515 (29 August - 1 September 2016, Miȩdzyzdroje, Poland)
4. Kowalewski, A., Lasiecka, I., Sokołowski, J.: Sensitivity analysis of hyperbolic optimal control problems. Computational Optimization and Applications 52, 147–179 (2012)
5. Kowalewski, A., Krakowiak, A.: Optimal boundary control problem of retarded parabolic systems. Archives of Control Sciences 23, 261–279 (2013)
6. Lions, J.L.: Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin-Heidelberg (1971)
7. Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications. Springer-Verlag, Berlin-Heidelberg, vol. 1 and 2 (1972)
8. Sokołowski, J., Żochowski. A.: Modelling of topological derivatives for contact problems. Numerische Mathematik 102, 145–179 (2005)
Acknowledgements
The research presented here was carried out within the research programme AGH University of Science and Technology, No. 11.11.120.396.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Kowalewski, A., Emirsajłow, Z., Sokołowski, J., Krakowiak, A. (2017). Sensitivity Analysis of Optimal Control Parabolic Systems with Retardations. In: Mitkowski, W., Kacprzyk, J., Oprzędkiewicz, K., Skruch, P. (eds) Trends in Advanced Intelligent Control, Optimization and Automation. KKA 2017. Advances in Intelligent Systems and Computing, vol 577. Springer, Cham. https://doi.org/10.1007/978-3-319-60699-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-60699-6_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60698-9
Online ISBN: 978-3-319-60699-6
eBook Packages: EngineeringEngineering (R0)