Boundary Stabilization with restricted observability

TL;DR

This paper investigates boundary stabilization of hyperbolic conservation law systems with limited boundary observability, demonstrating how restricted observations impact control strategies and system stabilization, with applications to flow models.

Contribution

It introduces a stabilization approach under restricted boundary observability, applying boundary control directly on observed variables and analyzing its effects on different models.

Findings

Restricted observability can limit control effectiveness

Boundary control on observed variables can stabilize certain systems

Limited observation may prevent stabilization in some cases

Abstract

Lyapunov functions are popularly used to investigate the stabilization problem of systems of hyperbolic conservation laws with boundary controls. In real life applications often not every boundary value can be observed. In this work, we show the stabilization under a restricted boundary observability. Thereby, we apply the boundary control directly on the observed (physical) variables. Using well-known stabilization results from the literature, we also discuss examples such as a density flow model or the Saint-Venant equations. This shows that a restricted observation can result in more restrictive control choices or can prevent the system from stabilizing.