5 citations · 7 across the 2 of their papers we have counts for
6 papers
Galerkin approximations for the optimal control of nonlinear delay differential equations
Mickaël D. Chekroun, Axel Kröner, Honghu Liu
Optimal control problems of nonlinear delay differential equations (DDEs) are considered for which we propose a general Galerkin approximation scheme built from Koornwinder polynom…
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Mickaël D. Chekroun, Axel Kröner, Honghu Liu
Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in…
Optimal control of PDEs in a complex space setting; application to the Schrödinger equation
M. Soledad Aronna, Frédéric Bonnans, Axel Kröner
In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup stru…
Optimal control of infinite dimensional bilinear systems: Application to the heat and wave equations
M. Soledad Aronna, Frédéric Bonnans, Axel Kröner
In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the control entering linea…
Numerical approximation of level set power mean curvature flow
Axel Kröner, Eva Kröner, Heiko Kröner
In this paper we investigate the numerical approximation of a variant of the mean curvature flow. We consider the evolution of hypersurfaces with normal speed given by , $k \g…
Local minimization algorithms for dynamic programming equations
Dante Kalise, Axel Kröner, Karl Kunisch
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimizati…