Stabilization of Partial Differential Equations by Sequential Action Control
Optimization and Control
2022-08-30 v4
Abstract
We present a framework of sequential action control (SAC) for stabilization of systems of partial differential equations which can be posed as abstract semilinear control problems in Hilbert spaces. We follow a late-lumping approach and show that the control action can be explicitly obtained from variational principles using adjoint information. Moreover, we analyze the closed-loop system obtained from the SAC feedback for the linear problem with quadratic stage costs. We apply this theory to a prototypical example of an unstable heat equation and provide numerical results as the verification and demonstration of the framework.
Cite
@article{arxiv.1905.11717,
title = {Stabilization of Partial Differential Equations by Sequential Action Control},
author = {Yan Brodskyi and Falk M. Hante and Arno Seidel},
journal= {arXiv preprint arXiv:1905.11717},
year = {2022}
}