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This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer the system towards a desired state. The presented approach is based on a Lyapunov stability analysis and a CWENO-type reconstruction.

This work is devoted to the Galerkin projection of highly nonlinear random quantities. The dependency on a random input is described by Haar-type wavelet systems. The classical Haar sequence has been used by Pettersson, Iaccarino, Nordstroem (2014) for a hyperbolic stochastic Galerkin formulation of the one-dimensional Euler equations. This work generalizes their approach to several multi-dimensional systems with Lipschitz continuous and non-polynomial flux functions. Theoretical results are illustrated numerically by a genuinely multidimensional CWENO reconstruction.

We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the level-set equations. A novel intrusive Galerkin formulation is presented and proven hyperbolic. It induces a corresponding finite-volume scheme that is specifically taylored for uncertain velocities.

We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are projected to obtain a deterministic system for the coefficients in the truncated series. Stochastic Galerkin formulations are presented in conservative form and for smooth solutions also in the corresponding non-conservative form. This allows to obtain stabilization results, when the system is relaxed to a first-order model. Computational tests illustrate the theoretical results.

We consider linear hyperbolic balance law that describe gas flow. Stochastic influences are introduced by series of orthogonal functions. A deterministic stabilization concept, which makes deviations at steady states decay exponentially fast, is extended to stochastic influences. These can be described by general Gaussian processes. The computational complexity, however, may prevent an application to certain random fields., Comment: The article is replaced by arXiv:2007.00526

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.