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- Title
Stabilization of infinite-dimensional linear evolution equations with self-adjoint generator by using a POD reduced-order Riccati feedback.
- Authors
Trélat, Emmanuel; Wang, Gengsheng; Xu, Yashan
- Abstract
There are many methods to stabilize an infinite-dimensional linear autonomous control system which is stabilizable. The challenge is to find a exponentially stabilizing feedback control that is as simple as possible. Riccati theory provides a nice feedback control, but numerically solving Riccati equations may be difficult for infinite-dimensional control systems. The Proper Orthogonal Decomposition (POD) offers a popular method to reduce large-dimensional systems. In the present paper, we show that, under appropriate assumptions, a Riccati feedback law derived from a finite-dimensional system obtained by the POD method stabilizes the infinite-dimensional system.
- Subjects
PROPER orthogonal decomposition; LINEAR control systems; RICCATI equation; EVOLUTION equations; LINEAR equations
- Publication
Mathematical Control & Related Fields, 2024, Vol 14, Issue 4, p1
- ISSN
2156-8472
- Publication type
Academic Journal
- DOI
10.3934/mcrf.2024057