Computational methods for boundary optimal control and identification problems

Axelsson, Owe; Béreš, Michal; Blaheta, Radim

doi:10.1016/j.matcom.2021.02.019

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…A particularly important class of problems concern inverse problems, where an optimal control framework can be used. Examples include parameter estimation [47] and finding inaccessible boundary conditions [48], where a PRESB type preconditioner has been used.…”

Section: A Basic Class Of Optimal Control Problemsmentioning

confidence: 99%

Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

Axelsson

Karátson

2020

Numer. Math.

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Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties, such as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.

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Section: A Basic Class Of Optimal Control Problemsmentioning

confidence: 99%

Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

Axelsson

Karátson

2020

Numer. Math.

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“…To solve this problem, scholars have carried out many research works and proposed various optimal control algorithms. 29–32 Gavrikov et al 33 study the optimal boundary control problem with linear quadratic cost function in the heat transfer process of a cylinder; Mechelli and Volkwein 34 study an optimal boundary and bilateral control problem of heat transfer equation with convection term; Dekhkonov 35 recently studies the boundary control problem, based on the heat transfer model, for the heat exchange process; Bollo et al 36 solve OCPs of Neumann boundary for a n -dimensional heat equation; Abbasi and Malek 37 solve pointwise optimal control problem on and inside a tissue subject to thermal wave model with Dirichlet and Rubin boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Parameterization optimal control of an unsteady partial differential equations with convection term by an improved three-term spectrum conjugate gradient algorithm

Yu,

Wang,

Pang

et al. 2023

Measurement and Control

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The unsteady partial differential equations (UPDE) with convection term gives a clear descriptions for the solidification process of a slab in dynamic production of continuous casting. To give a suitable setting value of secondary cooling water flow rate for the dynamic control system, this study investigates an optimal control problem (OCP) of UPDE with convection term. Firstly, control vector discretization of OCP and the solution of UPDE are given. Secondly, due to the rapidity for gradient, this paper analyzes the expression of the gradient calculation method based on Hamiltonian function costate system by approximate treatment, matrix calculation and composite trapezoidal integral method. Thirdly, an improved three-term spectrum conjugate gradient algorithm (ITSCGA) is proposed to solve the OCP of UPDE, and the global convergence of the ITSCGA is demonstrated. Lastly, the performance of ITSCGA is demonstrated by experimental simulations. The results demonstrate that the ITSCGA provides a smaller temperature fluctuations, and improves the quality of a slab.

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“…This furnishes a significant interest over ODE models, whose capacity to describe spatial information is limited by the number of spatial compartments that the model includes. Our contribution consists in a boundary optimal control problem [24][25][26][27] subject to an SIR-diffusion model describing a time-space spread of a disease. The constraint is a system of three PDEs with Dirichlet and Neumann boundary condition concerning the S and R unknown.…”

Section: Introductionmentioning

confidence: 99%

Boundary optimal control of time–space SIR model with nonlinear Robin boundary condition

Essoufi

Zafrar

2021

Int. J. Dynam. Control

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Computational methods for boundary optimal control and identification problems

Cited by 6 publications

References 13 publications

Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

Parameterization optimal control of an unsteady partial differential equations with convection term by an improved three-term spectrum conjugate gradient algorithm

Boundary optimal control of time–space SIR model with nonlinear Robin boundary condition

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