14 research outputs found
An adaptive POD approximation method for the control of advection-diffusion equations
We present an algorithm for the approximation of a finite horizon optimal
control problem for advection-diffusion equations. The method is based on the
coupling between an adaptive POD representation of the solution and a Dynamic
Programming approximation scheme for the corresponding evolutive
Hamilton-Jacobi equation. We discuss several features regarding the adaptivity
of the method, the role of error estimate indicators to choose a time
subdivision of the problem and the computation of the basis functions. Some
test problems are presented to illustrate the method.Comment: 17 pages, 18 figure
Recent results in shape optimization and optimal control for PDEs
In this paper we will present some recent advances in the numerical approximation of two classical problems: shape optimization and optimal control for evolutive partial differential equations. For shape optimization we present two novel techniques which have shown to be rather efficient on some applications. The first technique is based on multigrid methods whereas the second relies on an adaptive sequential quadratic programming. With respect to the optimal control of evolutive problems, the approximation is based on the coupling between a POD representation of the dynamical system and the classical Dynamic Programming approach. We look for an approximation of the value function characterized as the weak solution (in the viscosity sense) of the corresponding Hamilton-Jacobi equation. Several tests illustrate the main features of the above methods