Stabilization of partial differential equations by sequential action control

Brodskyi Y, Hante FM, Seidel A (2022)

Publication Type: Journal article

Publication year: 2022

Journal

IMA Journal of Mathematical Control and Information Oxford University Press (OUP): Policy A - Oxford Open Option A

DOI: 10.1093/imamci/dnac021

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 analyse 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.

Involved external institutions

Humboldt-Universität zu Berlin DE Germany (DE)

How to cite

APA:

Brodskyi, Y., Hante, F.M., & Seidel, A. (2022). Stabilization of partial differential equations by sequential action control. IMA Journal of Mathematical Control and Information. https://doi.org/10.1093/imamci/dnac021

MLA:

Brodskyi, Yan, Falk M. Hante, and Arno Seidel. "Stabilization of partial differential equations by sequential action control." IMA Journal of Mathematical Control and Information (2022).

BibTeX: Download