Minimax Control of Parabolic Systems with Dirichlet Boundary Conditions and State Constraints |
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Authors: | Mordukhovich B S Zhang K |
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Institution: | (1) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA boris@math.wayne.edu, zhang@math.wayne.edu, US |
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Abstract: | In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet
boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence
theorem for minimax solutions and develop effective penalized procedures to approximate state constraints. Based on a careful
variational analysis, we establish convergence results and optimality conditions for approximating problems that allow us
to characterize suboptimal solutions to the original minimax problem with hard constraints. Then passing to the limit in approximations,
we prove necessary optimality conditions for the minimax problem considered under proper constraint qualification conditions.
Accepted 7 June 1996 |
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Keywords: | , Approximations, Constraint qualification, Dirichlet boundary controls, Minimax criterion, Parabolic equations,,,,,,State constraints, Uncertain disturbances, Variational inequalities, AMS Classification, Primary 49K20, 49K35, Secondary 49J20,,,,,,35K50, |
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