We study the problem of constructing asymptotically optimal meshes with respect to the gradient error of a given input function. We provide simpler proofs of previously known results and show constructively that a closed-form solution exists for them. We show how the transformational method for obtaining meshes, as is, cannot produce asymptotically optimal meshes for general inputs. We also dis...

We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non-discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introd...

A globalization strategy for multigrid schemes solving optimal control problems is presented. This approach searches for possible negative eigenvalues of the reduced Hessian considered at the coarsest grid of the multigrid process. If negative eigenvalues are detected, a globalization step in the direction of negative curvature is performed to escape undesired maxima or saddle points. It is sho...

Difference equations of the form X ( t ) = F * ( t ) X ( t 1 ) F ( t ) F * ( t ) X ( t 1)G(t)[ l + G * ( t ) X ( t 1)G(t)]t G * ( t ) X ( t 1)F(t)+ Q(t ) and their associated Hermitian matrices H ( t ) = (0 v F* _C,C.)(t) are studied. Solution of different Riccati equations can be compared if the difference of their corresponding Hermitian matrices is semidefinite for all t. An application to t...

This study presents a new finite element approximation for an optimal control problem (P ) governed by the heat equation and with end-point state constraints. The state constraint set S is assumed to have an empty interior in the state space. We begin with building a new penalty functional where the penalty parameter is an algebraic combination of the mesh size and the time step. Based on it, w...

A new optimal control control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced....

This work is devoted to the multiharmonic analysis of parabolic optimal control problems in a time-periodic setting. In contrast to previous approaches, we include the cases of different control and observation domains, the observation in certain energy spaces and the presence of control constraints. In all these cases we propose a new preconditioned MinRes solver for the frequency domain equat...

In this article, the minimum time control problem of an electric vehicle is modeled as a Mayer problem in optimal control, with affine dynamics with respect to the control and with state constraints. The candidates as minimizers are selected among a set of extremals, solutions of a Hamiltonian system given by the maximum principle. An analysis, with the techniques of geometric control, is used ...

Two families of 4-phase sequences are constructed using irreducible polynomials over Z4. Family d has period L = 2' 1, size L +2, and maximum nontrivial correlation magnitude C,,, 5 1 + m, where r is a positive integer. Family has period L = 2(2' l), size ( L + 2)/4, and C,,, 5 2 + m. Both families are asymptotically optimal with respect to the Welch lower bound on C,,, for complex-valued seque...