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- Title
Stabilization of partial differential equations by sequential action control.
- Authors
Brodskyi, Yan; Hante, Falk M; Seidel, Arno
- 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.
- Subjects
PARTIAL differential equations; CONTROL (Psychology); HEAT equation; HILBERT space; CLOSED loop systems
- Publication
IMA Journal of Mathematical Control & Information, 2022, Vol 39, Issue 4, p1008
- ISSN
0265-0754
- Publication type
Article
- DOI
10.1093/imamci/dnac021