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

Stabilization of infinite-dimensional linear evolution equations with self-adjoint generator by using a POD reduced-order Riccati feedback.

Trélat, Emmanuel; Wang, Gengsheng; Xu, Yashan