Adjoint concepts for the optimal control of Burgers equation

DOI10.1007/s10589-006-0393-7zbMath1278.49028OpenAlexW1988620958MaRDI QIDQ885820

Andrea Walther, Antje Noack

Publication date: 14 June 2007

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-006-0393-7

zbMATH Keywords

Newton's methodBurgers equationOptimal controlAutomatic differentiationAdjoint techniqueDiscrete adjoint

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) KdV equations (Korteweg-de Vries equations) (35Q53) Discrete approximations in optimal control (49M25) Flow control and optimization for incompressible viscous fluids (76D55)

Related Items

Distributed optimal control of the viscous Burgers equation via a Legendre pseudo-spectral approach ⋮ Optimal boundary control of the unsteady Burgers equation with simultaneous space-time discretization ⋮ Optimal control and optimality condition of the Camassa-Holm equation ⋮ A novel approach of unsteady adjoint lattice Boltzmann method based on circular function scheme ⋮ Unnamed Item ⋮ Solving optimal control problems for the unsteady Burgers equation in COMSOL multiphysics ⋮ Adjoint Code Design Patterns ⋮ Necessary optimality conditions for optimal distributed and (Neumann) boundary control of Burgers equation in both fixed and free final horizon cases ⋮ A numerical approach to an optimal boundary control of the viscous Burgers' equation ⋮ Sensitivity analysis approach for reduced-order approximations of optimal control problems governed by Burgers equation ⋮ An all-at-once approach for the optimal control of the unsteady Burgers equation ⋮ (non)uniqueness of critical points in variational data assimilation

Uses Software

• ADOL-C
• Matlab
• revolve
• ADIFOR
• FADBAD++
• ADMAT
• TAMC
• TAF

Cites Work

• Evaluating gradients in optimal control: continuous adjoints versus automatic differentiation
• Boundary control of Burgers' equation -- a numerical approach
• Analysis of instantaneous control for the Burgers equation
• Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
• The lagrange-newton method for infinite-dimensional optimization problems
• Recipes for adjoint code construction
• The SQP method for control constrained optimal control of the Burgers equation
• Algorithm 755: ADOL-C
• Algorithm 799: revolve
• On the Lagrange--Newton--SQP Method for the Optimal Control of Semilinear Parabolic Equations
• Parallel Lagrange--Newton--Krylov--Schur Methods for PDE-Constrained Optimization. Part I: The Krylov--Schur Solver
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item