Existence theorems for an optimal control problem relative to a linear, hyperbolic partial differential equation

1971 ◽  
Vol 7 (2) ◽  
pp. 109-117 ◽  
Author(s):  
G. Pulvirenti
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence Theorems ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential

Sparse Grid Collocation Method for an Optimal Control Problem Involving a Stochastic Partial Differential Equation with Random Inputs

2014 ◽  
Vol 4 (2) ◽  
pp. 166-188 ◽  
Author(s):  
Nary Kim ◽  
Hyung-Chun Lee
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Collocation Method ◽  
Galerkin Approximation ◽  
Random Coefficients ◽  
Sparse Grid ◽  
Partial Differential

AbstractIn this article, we propose and analyse a sparse grid collocation method to solve an optimal control problem involving an elliptic partial differential equation with random coefficients and forcing terms. The input data are assumed to be dependent on a finite number of random variables. We prove that an optimal solution exists, and derive an optimality system. A Galerkin approximation in physical space and a sparse grid collocation in the probability space is used. Error estimates for a fully discrete solution using an appropriate norm are provided, and we analyse the computational efficiency. Computational evidence complements the present theory, to show the effectiveness of our stochastic collocation method.

Parallel D–D type domain decomposition algorithm for optimal control problem governed by parabolic partial differential equation

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Bo Zhang ◽  
Jixin Chen ◽  
Danping Yang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Domain Decomposition ◽  
Decomposition Algorithm ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Domain Decomposition Algorithm

AbstractA parallel domain decomposition algorithm for solving an optimal control problem governed by a parabolic partial differential equation is proposed. This algorithm is based upon non-overlapping domain decomposition. In every iteration, the global problem is reduced to solve simultaneously some implicit subproblems on many sub-domains by using explicit flux approximations near inner-boundaries at each time-step. Both

scholarly journals Computing optimal control With a hyperbolic partial differential equation

1998 ◽  
Vol 40 (2) ◽  
pp. 266-287 ◽  
Author(s):  
V. Rehbock ◽  
S. Wang ◽  
K.L. Teo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Optimal Control ◽  
Automatic Differentiation ◽  
Gas Absorption ◽  
Hyperbolic Partial Differential Equations ◽  
Element Approximation ◽  
Hyperbolic Partial Differential Equation ◽  
Partial Differential ◽  
Rectangular Mesh

AbstractWe present a method for solving a class of optimal control problems involving hyperbolic partial differential equations. A numerical integration method for the solution of a general linear second-order hyperbolic partial differential equation representing the type of dynamics under consideration is given. The method, based on the piecewise bilinear finite element approximation on a rectangular mesh, is explicit. The optimal control problem is thus discretized and reduced to an ordinary optimization problem. Fast automatic differentiation is applied to calculate the exact gradient of the discretized problem so that existing optimization algorithms may be applied. Various types of constraints may be imposed on the problem. A practical application arising from the process of gas absorption is solved using the proposed method.

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