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Efficient algorithm to solve optimal boundary control problem for Burgers' equation

Alaeddin Malek, Roghayeh Ebrahim Nataj, Mohamad Javad Yazdanpanah (2012)

Kybernetika

In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method...

Error estimates for finite element approximations of elliptic control problems

Walter Alt, Nils Bräutigam, Arnd Rösch (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space

Pedro Merino, Fredi Tröltzsch, Boris Vexler (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.

Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems

Pedro Merino, Ira Neitzel, Fredi Tröltzsch (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.

Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints

Eduardo Casas (2002)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L ∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states....

Error Estimates for the Numerical Approximation of Semilinear Elliptic Control Problems with Finitely Many State Constraints

Eduardo Casas (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the L∞ norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states. ...

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