Linear Quadratic Regulator Computation for a Stefan Problem using M.-M.E.S.S. and FEniCS

This repository contains the code to reproduce the numerical experiments in the two papers "Riccati-feedback Control of a Two-dimensional Two-phase Stefan Problem" (paper_1) (https://arxiv.org/abs/2209.05476) and "Numerical integrators for non-autonomous closed-loop systems with Riccati-feedback" (paper_2) (http://arxiv.org/abs/2402.13656) and in the PhD thesis "Riccati Feedback Stabilization of the Stefan Problem" (thesis). In detail, the feedback gain matrices are computed in Matlab and the simulations in FEniCS.

Structure

DRE/ contains Matlab testing code for non-autonomous spliting and BDF methods.

Stefan_problem_simulation/ contains FEniCS testing code to simulate a 2D 2-phase Stefan problem with different controls and generate the time-dependent matrices for the non-autonomous DREs

Usage

Read the README files in DRE/ and Stefan_problem_simulation/.