Optimal control of impulsive stochastic evolution inclusions

N.U. Ahmed

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2002)

  • Volume: 22, Issue: 2, page 155-184
  • ISSN: 1509-9407

Abstract

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In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.

How to cite

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N.U. Ahmed. "Optimal control of impulsive stochastic evolution inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 22.2 (2002): 155-184. <http://eudml.org/doc/271434>.

@article{N2002,
abstract = {In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.},
author = {N.U. Ahmed},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {impulsive perturbations; C₀-semigroups; stochastic systems; differential inclusions; vector measures; optimal controls; impulse perturbations; -semigroups; optimal control},
language = {eng},
number = {2},
pages = {155-184},
title = {Optimal control of impulsive stochastic evolution inclusions},
url = {http://eudml.org/doc/271434},
volume = {22},
year = {2002},
}

TY - JOUR
AU - N.U. Ahmed
TI - Optimal control of impulsive stochastic evolution inclusions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2002
VL - 22
IS - 2
SP - 155
EP - 184
AB - In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
LA - eng
KW - impulsive perturbations; C₀-semigroups; stochastic systems; differential inclusions; vector measures; optimal controls; impulse perturbations; -semigroups; optimal control
UR - http://eudml.org/doc/271434
ER -

References

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  1. [1] N.U. Ahmed, Impulsive perturbation of C₀ semigroups and evolution inclusions, Nonlinear Functional Analysis and Applications, (to appear). 
  2. [2] N.U. Ahmed, Impulsive perturbation of C₀ semigroups and stochastic evolution inclusions, Discuss. Math. Differential Inclusions, Control and Optimization 22 (1) (2002), 125-149. Zbl1039.34055
  3. [3] N.U. Ahmed, Vector measures for optimal control of impulsive systems in Banach spaces, Nonlinear Functional Analysis and Applications 5 (2) (2000), 95-106. Zbl0982.49022
  4. [4] N.U. Ahmed, Some remarks on the dynamics of impulsive systems in Banach spaces, Dynamics of Continuous, Discrete and Impulsive Systems 8 (2001), 261-274. Zbl0995.34050
  5. [5] N.U. Ahmed, State dependent vector measures as feedback controls for impulsive systems in Banach spaces, Dynamics of Continuous, Discrete and Impulsive Systems 8 (2001), 251-261. Zbl0990.34056
  6. [6] N.U. Ahmed, Existence of solutions of nonlinear stochastic differential inclusions on Banach spaces, Proc. World Congress of Nonlinear Analysis' 92, (ed: V. Lakshmikantham), (1992), 1699-1712. 
  7. [7] N.U. Ahmed, Existence of optimal controls for a general class of impulsive systems on Banach spaces, SIAM Journal Contr. and Optim. (to appear). 
  8. [8] N.U. Ahmed, Necessary conditions of optimality for impulsive systems on Banach spaces, Nonlinear Analysis 51 (2002), 409-424. Zbl1095.49513
  9. [9] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, England 1992. Zbl0761.60052
  10. [10] J. Diestel and J.J. Uhl, Jr., Vector Measures, AMS, Mathematical Surveys 15 (1977). 
  11. [11] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Kluwer Academic Publishers, Dordrecht, Boston, London 1997. Zbl0887.47001
  12. [12] J.H. Liu, Nonlinear impulsive evolution equations, dynamics of continuous, Discrete and Impulsive Systems 6 (1999), 77-85. Zbl0932.34067
  13. [13] J. Motyl, On the solution of stochastic differential inclusions, J. Math. Anal. and Appl. 192 (1995), 117-132. Zbl0826.60053
  14. [14] A.M. Samoilenk and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore 1995. 
  15. [15] A.V. Skorohod, Studies in the Theory of Random Processes, (Eng. Trans), Addison-Wesley Publishing Company, Inc. Reading, Massachusetts, (1965), First published by Kiev University Press 1961. 
  16. [16] A.I. Tulcea and C.I. Tulcea, Topics in the Theory of Lifting, Springer-Verlag, Berlin, Heidelberg, New York 1969. Zbl0179.46303
  17. [17] T. Yang, Impulsive Control Theory, Springer-Verlag, Berlin 2001. Zbl0996.93003
  18. [18] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. 1, Fixed Point Theorems, Springer-Verlag New York, Berlin, Heidelberg, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest. Zbl0794.47033

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