Optimal Control of a Nutrient-Phytoplankton-Zooplankton-Fish System

Garvie, Marcus R.; Trenchea, Catalin

doi:10.1137/050645415

Cited by 59 publications

(21 citation statements)

References 33 publications

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“…Issues related to the analysis of numerical algorithms for optimal control problems constrained to time-dependent problems were studied in [2,8,10,17,19,22,[24][25][26][27][28]33,37,40,41,43,44]. In the recent works of [4,31,32,34,35] discontinuous Galerkin schemes were analyzed for distributed optimal control problems constrained to linear parabolic PDE's.…”

Section: Related Resultsmentioning

confidence: 99%

Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

Chrysafinos

2009

ESAIM: M2AN

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Abstract.A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE's is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions of the continuous optimality system is shown. The proof is based on stability estimates at arbitrary time points under minimal regularity assumptions, and a discrete compactness argument for discontinuous Galerkin schemes (see Walkington [SINUM (June 2008) (submitted), preprint available at

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Section: Related Resultsmentioning

confidence: 99%

Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

Chrysafinos

2009

ESAIM: M2AN

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“…When a cost functional measuring the discrepancy between solutions and target functions is formulated, constrained optimization techniques are employed (one-shot, sensitivity or adjoint-based methods) to construct an iterative algorithm [10,29] for estimating model parameters. There are numerous works in the literature that apply optimal control theory to reaction-diffusion systems [4][5][6]8,12,13,16,19,20,45]. However, relatively few works focus on estimating parameters in nonlinear reaction-diffusion systems [1,14,24,28], and to the best of our knowledge, none address parameter estimation for the Turing reaction-diffusion model.…”

Section: Introductionmentioning

confidence: 99%

An efficient and robust numerical algorithm for estimating parameters in Turing systems

Garvie

Maini

Trenchea

2010

Journal of Computational Physics

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a b s t r a c tWe present a new algorithm for estimating parameters in reaction-diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer-Meinhardt reaction-diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.

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“…The optimal control problem for the reaction diffusion model is studied in many papers( [2], [4], [5], [9]). In particular, Ryu and Yagi [9] studied the optimal control problem for the chemotaxis model of non-monotone type.…”

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confidence: 99%