This article is cited in 2 papers

On the explicit scheme with variable time steps for solving the parabolic optimal control problem

A. D. Romanenko

Kazan Federal University, Kazan, 420008 Russia

Abstract: The paper deals with the optimal control problem, including the linear parabolic equation as a state problem. Pointwise constraints are imposed on the control function. The objective functional involves the observation function in the entire space-time domain. The optimal control problem is approximated by a finite dimensional problem with mesh approximation of the state equation by the explicit (forward Euler) mesh scheme with variable time steps. The existence of unique solutions for the continuous and mesh optimal control problems is proved. The Uzawa-type iterative method is used for solving the finite dimensional optimal control problem. The results of numerical experiments are presented.

Keywords: optimal control, constraint on control, variable step, iterative method.

UDC: 519.63+517.977.58

Received: 10.05.2016

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