An efficient computational method for the optimal control problem for the Burgers equation

Küçük, İsmail; Sadek, Ibrahim

doi:10.1016/j.mcm.2006.03.002

Cited by 13 publications

(10 citation statements)

References 16 publications

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“…Their eventual purpose is to extend this technique to the control problems of viscous fluid flows [54]. As far as we know, other papers were also devoted to its study of [55][56][57][58][59][60] and the citations therein were also devoted its study. Apart for the case of the Burgers equation, there are plenty of researches concerned with other optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of the viscous Dullin–Gottwalld–Holm equation

Shen

Gao

2010

Nonlinear Analysis: Real World Applications

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Section: Introductionmentioning

confidence: 99%

Optimal control of the viscous Dullin–Gottwalld–Holm equation

Shen

Gao

2010

Nonlinear Analysis: Real World Applications

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“…This method generalizes an approach studied in the mid-1980s to solve optimal control problems for systems described by ordinary differential equations [18] to partial differential equations, in a similar manner as has been done for sheet and film processes (e.g., see [6], and citations therein) as well as nonlinear PDEs such as Burgers equation [9]. To apply this method, start with the analytical solution to the PDE (4)-(7)…”

Section: Basis Function Expansionmentioning

confidence: 99%

“…For example, in the case where a single control variable is spatially distributed throughout the domain, 100 discretization points in each spatial dimension and in time results in 100 4 = 10 8 degrees of freedom in the algebraic optimization. This large dimensionality problem is well recognized in the optimal control literature (e.g., [9], [18]). While many approaches have been proposed, no single algorithm dominates either the literature or applications and it is generally accepted that the best approach depends on the details on the optimal control problem being solved.…”

Section: Problem Setupmentioning

confidence: 99%

Optimal control of cellular uptake in tissue engineering

Kishida¹,

Ford²,

Pack³

et al. 2008

2008 American Control Conference

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The optimal control of a distributed parameter system with reaction, diffusion, and convection is investigated. The problem is motivated by tissue engineering where the control of the uptake of growth factors (signaling molecules) is required to spatially and temporally regulate cellular processes for the growth or regeneration of a tissue. Four approaches for solving the optimal control problem are compared: (i) basis function expansion, (ii) method of moments, (iii) internal model control, and (iv) model predictive control. This comparison suggests that these approaches should be combined to solve the optimal control problem for multiple spatial dimensions.

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“…Pugh [149] determined that the Galerkin/conservation method are more accurate and compute more quickly than the Galerkin method for the Burgers equation with neumann boundary conditions. Kucuk and Sadek [150] presented an efficient numerical scheme for the optimal control of the Burgers equation by means of point-wise actuators in the spatial domain. The study also pointed that the location of actuators can play a crucial role if they are not calculated optimally.…”

Section: Survey Of Different Techniquesmentioning

confidence: 99%