Exponential stability of PI control for Saint-Venant equations with a friction term

Georges Bastin (1) , Jean-Michel Coron (2, 3, 4)

1 CSAM - Centre for Systems Engineering and Applied Mechanics
2 SU - Sorbonne Université
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 CaGE - Control And GEometry

We consider open channels represented by Saint-Venant equations that are monitored and controlled at the downstream boundary and subject to unmeasured flow disturbances at the upstream boundary. We address the issue of feedback stabilization and disturbance rejection under Proportional-Integral (PI) boundary control. For channels with uniform steady states, the analysis has been carried out previously in the literature with spectral methods as well as with Lyapunov functions in Riemann coordinates. In this article, our main contribution is to show how the analysis can be extended to channels with non-uniform steady states with a Lyapunov function in physical coordinates.

Domaines: Optimisation et contrôle [math.OC]

Georges Bastin, Jean-Michel Coron. Exponential stability of PI control for Saint-Venant equations with a friction term. Methods and Applications of Analysis, 2019, 26 (2), pp.101-112. ⟨hal-01956634⟩