Controllability of evolution equations and inclusions driven by vector measures

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

Abstrakty

EN

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.

Słowa kluczowe

EN

controlability; impulsive systems; differential inclusions; Hilbert spaces; vector valued measures; C₀ semigroups

Kategorie tematyczne

• 34K30: Equations in abstract spaces
• 93C25: Systems in abstract spaces
• 35B30: Dependence of solutions on initial and boundary data, parameters
• 34G20: Nonlinear equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2004
• Tom: 24
• Numer: 1
• Strony: 49-72

Daty

wydano

2004

otrzymano

2004-06-01

Twórcy

autor

N.U. Ahmed

• School of Information Technology and Engineering and Department of Mathematics, University of Ottawa, Ottawa, Ontario K1N6N5

Bibliografia

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• [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.
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• [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.
• [18] M. Kisielewicz, M. Michta and J. Motyl, Set Valued Approach to Stochastic Control (II): Viability and Semimartingale Issues, Dynamic Systems and Applications 12 (2003), 433-466.

Identyfikatory

DOI

10.7151/dmgt.1052