engleski

Optimal Control of Parabolic Equations -- a Numerical Case Study in Periodic Homogenization

We consider an optimal control problem for a general linear parabolic equation governed by a self-adjoint operator on an abstract Hilbert space. The task consists in identifying a control (entering the system through the initial condition) that minimizes the distance of the trajectory of the system from a given constraint while steering the final state at time $T > 0$ close to the given target. First, we obtain the closed form solution for several types of trajectory constraints. Then second we present a numerical scheme based on the award wining \texttt{; ; rkfit}; ; algorithm for approximating the trajectory of the system using spectral calculus and a rational function surrogate. As a test of the robustness of the method we study the asymptotic behavior, in the homogenization limit, of a sequence of optimal control problems for parabolic equations with rapidly oscillating coefficients. This talk is based on joint work with Martin Lazar, Ivica Nakić and Martin Tautenhahn.

functional calculus, control theory, finite elements, numerical homogenization

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