arXiv subjects

Eduardo Casas

Publications and source records attributed to Eduardo Casas.

22 records · Page 2Linked to original sources

arXiv2018

Optimal time delays in a class of reaction-diffusion equations

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.

math.OC↗

arXiv2018

Measure Control of a Semilinear Parabolic Equation with a Nonlocal Time Delay

We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional includes a non-differentiable term with the measure-norm of the control. Existence, uniqueness and regularity of the solution of the state equation, as well as differentiability properties of the control-to-state operator are obtained. Next, we provide first order optimality conditions for local solutions. Finally, the control space is suitably discretized and we prove convergence of the solutions of the discrete problems to the solutions of the original problem. Several numerical examples are included to illustrate the theoretical results.

math.OC↗

arXiv2017

Analysis of optimal control problems of semilinear elliptic equations by BV-functions

Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of optimal controls, necessary and suffcient optimality conditions of first and second order are analysed. Special attention is paid on the effect of the choice of the vector norm in the definition of the BV-seminorm for the optimal primal and adjoined variables.

math.OC↗

arXiv2017

Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems

We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in $L^1$. In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization, and prove error estimates of bang-bang controls in $L^1$-norms.

math.OC↗