# Poster Session and Reception

Tuesday, March 15, 2016 - 4:00pm - 6:00pm

Lind 400

**Boundary Feedback Control of Shallow Water Flow**

Ben Mansour Dia (King Abdullah University of Science & Technology)

We present boundary feedback control laws for the linearized shallow water model for stabilization around a given steady state. The control objective is to bring the water volume to the equilibrium as faster as possible by means of local boundary conditions.**Mean Field Game for Marriage**

Ben Mansour Dia (King Abdullah University of Science & Technology)

The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. We describe a unique paradigm for preserving relationships and marital stability from mean field game theory.**Variational Multi-Scale Method with Spectral Approximation of the Sub-scales**

Ben Mansour Dia (King Abdullah University of Science & Technology)

A variational multi-scale method where the sub-grid scales are computed by spectral approximations is presented. It is based upon an extension of the spectral theorem to non-necessarily self-adjoint elliptic operators that have an associated base of eigenfunctions which are orthonormal in weighted L2 spaces.**New Second-order Time Schemes for Optimal Control of PDEs**

Jun Liu (Jackson State University)

We will present two new second-order time schemes as follows:

(1) A new second-order leapfrog scheme in time with a multigrid solver is proposed for solving the forward-backward optimality KKT system of the parabolic optimal control problems.

(2) A new second-order implicit scheme in time with a preconditioned GMRES solver is developed for solving the forward-backward optimality KKT system of the hypebolic wave optimal control problems.**Feedback Control of Thin Films**

Susana Gomes (Imperial College London)

Thin liquid films flowing down inclined walls are an example of physical phenomena that have a rich range of dynamical behaviour and therefore act as a paradigm for understanding transitions between different types of dynamical behaviour. In addition to that, they also have a wide range of industrial applications such as coating and heat transfer. Very thin films are usually stable and therefore flat, but as the film thickness is increased beyond a critical value depending on a slope angle, inertial effects give rise to waves that travel down the slope, and can eventually become chaotic.

We present a linear feedback control methodology that aims to drive the flow to any trajectory in the range of solutions (either the flat solution or travelling wave solutions) of this problem, analysing its effect in various models: weakly nonlinear models such as the so-called Kuramoto-Sivashinsky equation and two reduced order long-wave models (the Benney equation and the first order weighted-residuals model). When possible, we also compare the results obtained with linear stability results for the full (2D) Navier-Stokes equations.**Information Quantification for Data Assimilation**

Sarah King (Naval Research Laboratory)

We discuss the application of observability to the planning of sensor congurations in numerical weather prediction (NWP). The dimensions used in NWP make conventional denitions of observability impractical. For this reason we will rely partial observability which is obtained using dynamic optimization to approximate the observability. Using this metric we form an optimization problem to select sensor congurations that maximize the partial observability of the dynamical system. This leads to a max-min problem which using an empirical gramian matrix we reduce to an eigenvalue optimization problem.

Atmospheric data assimilation is the process of combining prior knowledge with observations to form an estimate of the system state required to produce a forecast of future weather conditions. Optimal sensor congurations leading to improved forecast quality are of interest. Due to the potential size of our intended application we will focus on computational methods that are both effcient and scalable. We also discuss applications to data thinning.**Optimal Control and Observation Locations for Time-Varying Systems on a Finite-Time Horizon**

Xueran Wu (Bergische Universität-Gesamthochschule Wuppertal (BUGH))

The choice of the location of controllers and observations is of great importance for designing control systems and improving the estimations in various practical problems. For time-varying systems in Hilbert spaces, the existence and convergence of the optimal locations based on the linear-quadratic control on a finite-time horizon is studied. The optimal location of observations for improving the estimation of the state at the final time, based on the Kalman filter, is considered as the dual problem to the LQ

optimal problem of the control locations. Further, the existence and convergence of optimal locations of observations for improving the estimation of the initial state, based on the Kalman smoother is discussed. The obtained results are applied to a linear advection-diffusion model with a special extension of emission rates.**Third Order Maximum-Principle-Satisfying Direct DG methods for Convection Diffusion Equations on Unstructured Triangular Mesh**

Jue Yan (Iowa State University)

We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods for convection diffusion equations on unstructured triangular mesh. We carefully calculate the normal derivative numerical flux across element edges and prove that, with proper choice of parameter pair in the numerical flux, the quadratic polynomial solution satisfies strict maximum principle. The polynomial solution is bounded within the given range and third order accuracy is maintained. There is no geometric restriction on the meshes and obtuse triangles are allowed in the partition. A sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximum-principle-satisfying limiter.**Identification of a Wave Equation Generated by a String**

Amin Boumenir (State University of West Georgia)

We show that we can identify and reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The reconstruction are based on Krein's inverse spectral theory for the first coefficient which is a Stieltjes measure and on the Gelfand-Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.**Quantifying Distributed Systems (Networks) Controllability**

Bassam Bamieh (University of California)

We reexamine the notions and distinctions between controllability and reachability for infinite dimensional systems. This distinction is not widely appreciated, however, it has recently emerged at the heart of the question of network controllability. I will argue that controllability and reachability are essentially diametrically opposite notions for systems with diffusive dynamics, but they are somewhat equivalent for advective systems. This translates to a similar distinction in network dynamics between undirected and directed networks respectively.**Stabilization of Piezoelectric Material?**

Matthias de Jong (Rijksuniversiteit te Groningen)

The application of piezoelectric material is widely applied in large mechanical structures and in high precision areas as well. Many modeling assumptions and approximation methods can be considered, when modeling piezoelectric material that influence stabilizability and system performance. This has been investigated recently and is continuously extended. Question remain on how the various modeling considerations influence stability and system performance and what is the influence of the type of approximation?**Comparative Studies of Different Observers for Nonlinear Distributed Parameter Systems**

Sepideh Afshar (University of Waterloo)

The full state cannot be observed for distributed parameter systems. Although many observation methods have been developed for lumped parameter systems, fewer results are available for DPSs. In practice, a DPS model is approximated by a lumped model and then a method designed for the estimation of lumped systems is used. The issue of the effect of the neglected modes needs to be considered. In this presentation, a number of popular methods for estimation of nonlinear systems are compared: unscented Kalman filter (UKF), extended Kalman filtering (EKF), as well as a modified version of sliding mode observer (SMO). The three methods are compared for two different versions of the diffusion equation, a quasi-linear and a nonlinear diffusion equation. The methods are also compared for a nonlinear wave equation. All the comparisons are done with and without an external disturbance.**Robust Stabilization of Flows in Varying Regimes**

Jan Heiland (Max Planck Institute, Magdeburg)

The stabilization of laminar flows on the base of linearizations and feedback controllers has been the subject of many recent theoretical and computational studies. However, the applicability of the standard approaches is limited due to the inherent fragility of observer based controllers with respect to arbitrary small changes in the system. We show that a slight variation in the Reynolds number of a flow setup amounts to a coprime factor perturbation in the associated linear transfer function. Based on these findings, we argue that known concepts from robust control can be exploited to come up with an output feedback law that can stabilize the cylinder wake over the transition period from a stable to a stabilized regime.**Towards Optimal Feedback Control of High-dimensional Systems**

Dante Kalise (Johann Radon Institute for Computational and Applied Mathematics )**Reliability-constrained Robust Design Optimization for Multi-reservoir River Systems**

Nathan Gibson (Oregon State University)**Optimal Control of PDE on Graphs with Uncertain Boundary Data; Application to Gas Pipelines**

Anatoly Zlotnik (Los Alamos National Laboratory)**Error estimates for a stochastic collocation approach to parameter identification problems for random elliptic PDEs**

Catalin Trenchea (University of Pittsburgh)

We present a parameter identification problem constrained by PDEs with random input data. Several identification objectives are discussed that either minimize the expectation of a tracking cost functional or minimize the difference of desired statistical quantities in the appropriate $L^p$ norm. The stochastic parameter identification algorithm integrates an adjoint-based deterministic algorithm with the sparse grid stochastic collocation FEM approach. The proof of the error estimates uses a Fink-Rheinboldt theory.**Function Approximation in Reproducing Kernel Banach Space (RKBS)**

Jun Zhang (University of Michigan)