Controllability of evolution equations and inclusions driven by vector measures

N.U. Ahmed

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2004)

  • Volume: 24, Issue: 1, page 49-72
  • ISSN: 1509-9407

Abstract

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In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.

How to cite

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N.U. Ahmed. "Controllability of evolution equations and inclusions driven by vector measures." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 24.1 (2004): 49-72. <http://eudml.org/doc/271479>.

@article{N2004,
abstract = {In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.},
author = {N.U. Ahmed},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {controlability; impulsive systems; differential inclusions; Hilbert spaces; vector valued measures; C₀ semigroups; controllability; semilinear control systems; infinite-dimensional control systems; time-varying systems; countably additive nonnegative finite measure; Banach fixed point theorem},
language = {eng},
number = {1},
pages = {49-72},
title = {Controllability of evolution equations and inclusions driven by vector measures},
url = {http://eudml.org/doc/271479},
volume = {24},
year = {2004},
}

TY - JOUR
AU - N.U. Ahmed
TI - Controllability of evolution equations and inclusions driven by vector measures
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2004
VL - 24
IS - 1
SP - 49
EP - 72
AB - In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.
LA - eng
KW - controlability; impulsive systems; differential inclusions; Hilbert spaces; vector valued measures; C₀ semigroups; controllability; semilinear control systems; infinite-dimensional control systems; time-varying systems; countably additive nonnegative finite measure; Banach fixed point theorem
UR - http://eudml.org/doc/271479
ER -

References

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  15. [15] N.U. Ahmed, Semigroup Theory With Applications to Systems and Control, (1991), Pitman Research Notes in Mathematics Series, 246, Longman Scientific and Technical, U.K, Co-published with John Wiley, New York, USA. 
  16. [16] S. Hu and N.S. Papageorgiou, Hand Book of Multivalued Analysis, Vol.1, Theory, Kluwer Academic Publishers, Dordrecht, Boston, London 1997. 
  17. [17] M. Kisielewicz, M. Michta and J. Motyl, Set Valued Approach to Stochastic Control (I): Existence and Regularity Properties, Dynamic Systems and Applications 12 (2003), 405-432. Zbl1063.93047
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