Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control

N.U. Ahmed

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

  • Volume: 33, Issue: 1, page 89-109
  • ISSN: 1509-9407

Abstract

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In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.

How to cite

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N.U. Ahmed. "Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 33.1 (2013): 89-109. <http://eudml.org/doc/270646>.

@article{N2013,
abstract = {In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.},
author = {N.U. Ahmed},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {neutral differential equations; Banach spaces; optimal control; measure valued solutions},
language = {eng},
number = {1},
pages = {89-109},
title = {Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control},
url = {http://eudml.org/doc/270646},
volume = {33},
year = {2013},
}

TY - JOUR
AU - N.U. Ahmed
TI - Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2013
VL - 33
IS - 1
SP - 89
EP - 109
AB - In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.
LA - eng
KW - neutral differential equations; Banach spaces; optimal control; measure valued solutions
UR - http://eudml.org/doc/270646
ER -

References

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  2. [2] N.U. Ahmed, Measure solutions for semilinear evolution equations with polynomial growth and their optimal controls, Discuss. Math. Differential Inclusions 17 (1997), 5-27. 
  3. [3] N.U. Ahmed, Measure solutions for semilinear systems with unbounded nonlinearities, Nonlinear Analysis 35 (1998), 487-503. doi: 10.1016/S0362-546X(97)00699-8 
  4. [4] N.U. Ahmed, Relaxed solutions for stochastic evolution equations on Hilbert space with polynomial growth, Publicationes Mathematicae, Debrechen 54 (1-2) (1999), 75-101. 
  5. [5] N.U. Ahmed, Measure solutions for semilinear and quasilinear evolution equations and their optimal control, Nonlinear Analysis 40 (2000), 51-72. doi: 10.1016/S0362-546X(97)00699-8 Zbl0959.49019
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  7. [7] N.U. Ahmed, Deterministic and stochastic neutral systems on Banach spaces and their optimal Fedback controls, Journal of Nonlinear Systems and Applications (2009), 151-160. 
  8. [8] N.U. Ahmed, Measure solutions for evolution equations with discontinuous vector Fields, Nonlinear Functional Analysis & Applications 9 (3) (2004), 467-484. Zbl1075.34050
  9. [9] N.U. Ahmed, Optimal Stochastic Control of Measure Solutions on Hilbert Space, in Systems, Control, Modeling and Optimization (Edited by F. Ceragioli, A. Dontchev, H. Furuta, K. Marti & L. Pandolfi), Springer, (Proc. IFIP-TC7 Conference, Turin, Italy, 2005)), U.S., (2006), 1-12. 
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  18. [18] N.U. Ahmed, Some Recent Developments in Systems and Control Theory on Infinite Dimensional Banach Spaces, Part 1 & 2, Proceedings of the 5th International Conference on Optimization and Control with Applications, (Edited by: K.L. Teo, H. Xu and Y. Zhang), Beijing, China, 2012; Publisher: Springer-Verlag (in Print). 
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