Minimax control of parabolic systems with Dirichlet boundary conditions and state constraints

Mordukhovich BS & Zhang K (1997). Minimax control of parabolic systems with Dirichlet boundary conditions and state constraints. Applied Mathematics & Optimization 36 (3): 323-360. DOI:10.1007/s002459900066.

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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.

Item Type: Article
Uncontrolled Keywords: Approximations, Constraint qualification, Dirichlet boundary controls, Minimax criterion, Parabolic equations, State constraints, Uncertain disturbances, Variational inequalities.
Research Programs: Dynamic Systems (DYN)
Bibliographic Reference: Applied Mathematics and Optimization; 36:323-360 [1997]
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:08
Last Modified: 21 Sep 2016 13:03
URI: http://pure.iiasa.ac.at/5089

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