A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

DOI10.1080/00207179.2016.1178807zbMath1360.49022OpenAlexW2341060807MaRDI QIDQ2978046

Kamal Mamehrashi, Sohrab Ali Yousefi

Publication date: 21 April 2017

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207179.2016.1178807

zbMATH Keywords

diffusion equationRitz methodeigenfunction methodLegendre polynomial basisnonlinear two-dimensional optimal control

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Discrete approximations in optimal control (49M25)

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Application of the method of fundamental solutions for designing the optimal shape in heat transfer ⋮ Robust bivariate polynomials scheme with convergence analysis for two-dimensional nonlinear optimal control problem ⋮ Numerical solution of 2D fractional optimal control problems by the spectral method along with Bernstein operational matrix ⋮ Numerical solution of two-dimensional variable-order fractional optimal control problem by generalized polynomial basis ⋮ The Use of the Ritz Method and Laplace Transform for Solving 2D Fractional‐Order Optimal Control Problems Described by the Roesser Model

Cites Work

• Unnamed Item
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• Unnamed Item
• Robustness of operational matrices of differentiation for solving state-space analysis and optimal control problems
• A numerical technique for solving fractional optimal control problems
• Adaptive dynamic programming for control. Algorithms and stability
• A diffusion equation in transparent media
• A two-dimensional corner solution for a nonlinear diffusion equation
• A Chebyshev pseudospectral multidomain method for the soliton solution of coupled nonlinear Schrödinger equations
• Geometric approach for finding exact solutions to nonlinear partial differential equations
• Finite propagation speed for limited flux diffusion equations
• Determination of a time-dependent diffusivity from nonlocal conditions
• An Efficient Legendre Pseudospectral Method for Solving Nonlinear Quasi Bang-Bang Optimal Control Problems
• Determination of space–time-dependent heat source in a parabolic inverse problem via the Ritz–Galerkin technique
• Numerical solution of a class of two-dimensional quadratic optimal control problems by using Ritz method
• Distributed optimal control of the viscous Burgers equation via a Legendre pseudo-spectral approach
• Legendre multiscaling functions for solving the one-dimensional parabolic inverse problem
• Discretized quadratic optimal control for continuous-time two-dimensional systems
• Satisfier function in Ritz–Galerkin method for the identification of a time-dependent diffusivity