Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions

• Autorzy: N.U. Ahmed
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.

Słowa kluczowe

EN

impulsive perturbations; C₀-semigroups; stochastic systems; differential inclusions; vector measures; impulsive controls

Kategorie tematyczne

• 34K45: Equations with impulses
• 93C25: Systems in abstract spaces
• 93E03: Stochastic systems, general
• 93E20: Optimal stochastic control
• 49J27: Problems in abstract spaces
• 34G25: Evolution inclusions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 125-149

Daty

wydano

2002

otrzymano

2002-04-08

Twórcy

autor

N.U. Ahmed

• School of Information Technology and Engineering 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, Vector measures for optimal control of impulsive systems in Banach spaces, Nonlinear Functional Analysis and Applications 5 (2) (2000), 95-106.
• [3] 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.
• [4] 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.
• [5] 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.
• [6] N.U. Ahmed, Existence of optimal controls for a general class of impulsive systems on Banach spaces, SIAM Journal Contr. and Optim. (to appear).
• [7] N.U. Ahmed, Measure solutions impulsive evolutions differential inclusions and optimal control, Nonlinear Analysis 47 (2001), 13-23.
• [8] G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions, Cambridge University Press, Cambridge, England 1992.
• [9] S. Hu and N.S. Papageorgiou, Handbook of multivalued analysis, Kluwer Academic Publishers, Dordrecht, Boston, London 1997.
• [10] V. Lakshmikantham, D.D. Bainov and P.S. Simenov, Theory of impulsive differential equations, World Scientific, Singapore, London 1999.
• [11] J.H. Liu, Nonlinear impulsive evolution equations, dynamics of continuous, Discrete and Impulsive Systems 6 (1999), 77-85.
• [12] J. Motyl, On the solution of stochastic differential inclusions, J. Math. Anal. and Appl. 192 (1995), 117-132.
• [13] A.M. Samoilenk and N.A. Perestyuk, Impulsive differential equations, World Scientific, Singapore 1995.
• [14] T. Yang, Impulsive control theory, Springer-Verlag, Berlin 2001.
• [15] 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.

Identyfikatory

DOI

10.7151/dmgt.1035