Naslov
Optimal distributed control of the heat-type equations by spectral decomposition

Autori
Lazar, Martin ; Molinari, Cesare

Izvornik
Optimal control applications & methods (0143-2087) 42 (2021), 4; 891-926

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
optimal control ; parabolic equations ; spectral decomposition ; convex optimisation ; dual problem

Sažetak
We construct an algorithm for solving a constrained optimal control problem for a first order evolutionary system governed by a positive self- adjoint operator. The problem consists in identifying distributed control that minimises a given cost functional, which comprises a cost of the control and a trajectory regulation term, while steering the final state close to a given target. The approach explores the dual problem and it generalises the Hilbert Uniqueness Method (HUM). The practical implementation of the algorithm is based on a spectral decomposition of the operator determining the dynamics of the system. Once this decomposition is available −which can be done o✏ine and saved for future use−, the optimal control problem is solved almost instantaneously. It is practically reduced to a scalar non-linear equation for the optimal Lagrange multiplier. The efficiency of the algorithm is demonstrated through numerical examples corresponding to different types of control operators and penalisation terms.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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