engleski

Optimal control of parabolic equations - a spectral calculus based approach.

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 minimises a given cost functional, while steering the final state close to the given target. This can be considered as an inverse prob- lem (of initial source identification) for parabolic equations from the optimal control viewpoint. In order to efficiently deal with this problem, we propose a novel approach based on the spectral calculus for self adjoint operators and geometrical rep- resentation of the problem. We obtain closed form expression for the control solution as a function of the operator governing the dynamics of the system. Its numerical computation is performed by exploring efficient Krylov subspace tech- niques, by which one constructs a rational approximation of the aforementioned function of the operator. The efficiency of the proposed algorithm method is confirmed through nu- merical examples, which will be also presented.

Optimal control ; Parabolic equations ; spectral measures ; rational Krylov approximations

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