Feedback control for random, linear hyperbolic balance laws

TL;DR

This paper develops a control method for physical systems governed by random hyperbolic balance laws, using Lyapunov stability analysis to exponentially damp uncertainties, applicable to various systems including stochastic models.

Contribution

It introduces a novel control approach based on Lyapunov stability for random hyperbolic systems, accommodating a wide range of uncertainties and perturbations.

Findings

Control exponentially reduces uncertainty impact over time.

Method successfully applied to stochastic viscoplastic material model.

Applicable to diverse physical systems with random dynamics.

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.