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2002 | 22 | 2 | 155-184
Tytuł artykułu

Optimal control of impulsive stochastic evolution inclusions

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EN
Abstrakty
EN
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.
Twórcy
autor
  • SITE and Department of Mathematics, University of Ottawa, Ottawa, Ontario, Canada
Bibliografia
  • [1] N.U. Ahmed, Impulsive perturbation of C₀ semigroups and evolution inclusions, Nonlinear Functional Analysis and Applications, (to appear).
  • [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.
  • [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.
  • [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.
  • [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.
  • [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] 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] N.U. Ahmed, Necessary conditions of optimality for impulsive systems on Banach spaces, Nonlinear Analysis 51 (2002), 409-424.
  • [9] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, England 1992.
  • [10] J. Diestel and J.J. Uhl, Jr., Vector Measures, AMS, Mathematical Surveys 15 (1977).
  • [11] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Kluwer Academic Publishers, Dordrecht, Boston, London 1997.
  • [12] J.H. Liu, Nonlinear impulsive evolution equations, dynamics of continuous, Discrete and Impulsive Systems 6 (1999), 77-85.
  • [13] J. Motyl, On the solution of stochastic differential inclusions, J. Math. Anal. and Appl. 192 (1995), 117-132.
  • [14] A.M. Samoilenk and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore 1995.
  • [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] A.I. Tulcea and C.I. Tulcea, Topics in the Theory of Lifting, Springer-Verlag, Berlin, Heidelberg, New York 1969.
  • [17] T. Yang, Impulsive Control Theory, Springer-Verlag, Berlin 2001.
  • [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.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1036
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