Feedback control for random, linear hyperbolic balance laws

arXiv (Cornell University)

Abstract

We design the 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, as e.g. Gaussian processes. We illustrate the control effect on a stochastic viscoplastic material model.

Authors 4

1. Stephan Gerster Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik , RWTH Aachen University , Templergraben 55 , 52062 Aachen , Germany

   RWTH Aachen University

2. Markus� Bambach

   University of Zurich

   Affiliation as printed

   Institut für virtuelle Produktion , TH Zürich , Technoparkstraße 1 , 8005 Zürich , Switzerland

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 , Templergraben 55 , 52062 Aachen , Germany

4. Muhammad� Imran

   Brandenburg University of Technology Cottbus-Senftenberg

   Affiliation as printed

   Lehrstuhl Konstruktion und Fertigung , BTU Cottbus -Senftenberg , Konrad-Wachsmann-Allee 17 , 03046 Cottbus , Germany