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 minimizes 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 generalizes 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 offline and saved for future use– the optimal control problem is solved almost instantaneously. It is practically reduced to ascalar nonlinear equationfor theoptimalLagrangemultiplier. The efficiency of the algorithm is demonstrated through numerical examples corresponding to different types of control operators and penalization terms.

Optimal distributed control of linear parabolic equations by spectral decomposition

MOLINARI C
2021-01-01

Abstract

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 minimizes 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 generalizes 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 offline and saved for future use– the optimal control problem is solved almost instantaneously. It is practically reduced to ascalar nonlinear equationfor theoptimalLagrangemultiplier. The efficiency of the algorithm is demonstrated through numerical examples corresponding to different types of control operators and penalization terms.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1079938
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