FEEDBACK CONTROL FOR RANDOM, LINEAR HYPERBOLIC BALANCE LAWS

International Journal for Uncertainty Quantification, vol. 12, pp. 81–104

Abstract

We design boundary controls of physical systems that are faced by uncertainties. The system dynamics are described by random hyperbolic balance laws. The control aims to steer the system to a desired state under uncertainties. We propose a control based on Lyapunov stability analysis of a suitable series expansion of the random dynamics. The control damps the impact of uncertainties exponentially fast in time. The presented approach can be applied to a large class of physical systems and random perturbations (e.g., Gaussian processes). We illustrate the boundary control effect on a stochastic viscoplastic material model.

Authors 4

1. Markus� Bambach

   Institute of Virtual Manufacturing

   Affiliation as printed

   Institut für virtuelle Produktion, Zürich, Switzerland

2. Stephan Gerster Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany

3. Michaël Herty Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Germany

4. Muhammad� Imran

   Brandenburg University of Technology Cottbus-Senftenberg

   Affiliation as printed

   Lehrstuhl Konstruktion und Fertigung, BTU Cottbus-Senftenberg, Cottbus, Germany