Stabilization of infinite-dimensional linear control systems by POD reduced-order Riccati feedback

Emmanuel Trélat (1, 2) , Gengsheng Wang (3) , Yashan Xu (4)

1 CaGE - Control And GEometry
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 School of Mathematics and Statistics [Wuhan University]
4 School of Mathematical Sciences [Fudan]

There exist many ways to stabilize an infinite-dimensional linear autonomous control systems when it is possible. Anyway, finding an exponentially stabilizing feedback control that is as simple as possible may be a challenge. The Riccati theory provides a nice feedback control but may be computationally demanding when considering a discretization scheme. Proper Orthogonal Decomposition (POD) offers a popular way to reduce large-dimensional systems. In the present paper, we establish that, under appropriate spectral assumptions, an exponentially stabilizing feedback Riccati control designed from a POD finite-dimensional approximation of the system stabilizes as well the infinite-dimensional control system.

Mots clés: Riccati theory; linear quadratic optimal control; Feedback stabilization; Proper Orthogonal Decomposition (POD)

Domaines: Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Emmanuel Trélat, Gengsheng Wang, Yashan Xu. Stabilization of infinite-dimensional linear control systems by POD reduced-order Riccati feedback. 2019. ⟨hal-02163854⟩