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Nadir Arada (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an -space (). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.
Ahmed, N.U., Xiang, X. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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Lassana Samassi, Rabah Tahraoui (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: , (1) where is a set of admissible controls and is the solution of the following equation: ; . (2). The results are nonlocal and new.
Ahmed, N.U., Kerbal, Sebti (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Ahmed, N.U., Xiang, X. (1995)
Mathematical Problems in Engineering
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Anar Huseyin, Nesir Huseyin (2014)
Applications of Mathematics
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In this paper the control system with limited control resources is studied, where the behavior of the system is described by a nonlinear Volterra integral equation. The admissible control functions are chosen from the closed ball centered at the origin with radius in . It is proved that the set of trajectories generated by all admissible control functions is Lipschitz continuous with respect to for each fixed , and is continuous with respect to for each fixed...