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Time optimal control of the heat equation with pointwise control constraints

Karl Kunisch, Lijuan Wang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By Pontryagin’s maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained....

Time-optimal boundary control of an infinite order parabolic system with time lags

Adam Kowalewski, Anna Krakowiak (2008)

International Journal of Applied Mathematics and Computer Science

In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.

Topology optimization of systems governed by variational inequalities

Andrzej Myśliński (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper deals with the formulation of the necessary optimality condition for a topology optimization problem of an elastic body in unilateral contact with a rigid foundation. In the contact problem of Tresca, a given friction is governed by an elliptic variational inequality of the second order. The optimization problem consists in finding such topology of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. The topological derivative...

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