A Bayesian Approach to Feedback Control for Hyperbolic Balance Laws

arXiv (Cornell University)

Abstract

We propose a Bayesian framework for feedback boundary control of hyperbolic balance laws. The method propagates a probability distribution over feedback parameters using Lyapunov decay estimates as a likelihood. For linear models, it recovers available analytical stability results and extends to nonlinear regimes where theory is limited. Using first-order local Lax-Friedrichs (LLF) discretizations, we validate the approach on the decoupled wave system and the linearized Saint-Venant equations, reproducing known stability intervals and mixed boundary couplings. We then treat nonlinear and stochastic problems, including the nonlinear Saint-Venant system, one- and two-dimensional Burgers equations, Burgers equation with random initial data, and nonconservative perturbations with source terms, and show that the inferred stability domains are robust with respect to the indicator and the prior. Finally, we demonstrate transfer to a second-order semi-discrete LLF scheme and to a two-parameter feedback model for laser powder bed fusion with power regulation.

Authors 4

1. Markus Bambach

   ETH Zurich

   Affiliation as printed

   Department of Mechanical and Process Engineering , ETH Zürich , Zürich , 8005 , Switzerland;

2. Shaoshuai Chu Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics , RWTH Aachen University , Aachen , 52056 , Germany;

3. Michaël Herty Aachen Department of Mathematics

   University of Pretoria · RWTH Aachen University

   Affiliation as printed

   Department of Math- ematics and Applied Mathematics , University of Pretoria , Private Bag X20 , Hatfield 0028 , South Africa;

   Department of Mathematics , RWTH Aachen University , Aachen , 52056 , Germany;

4. Yunong Lin

   ETH Zurich

   Affiliation as printed

   Department of Mechanical and Process Engineering , ETH Zürich , Zürich , 8092 , Switzerland;