Physical Sciences and Mathematics Commons^™

Analysis Of Transient Growth In Iterative Learning Control Using Pseudospectra, Douglas A. Bristow, John R. Singler

Mechanical and Aerospace Engineering Faculty Research & Creative Works

In this paper we examine the problem of transient growth in Iterative Learning Co ntrol (ILC). Transient growth is generally avoided in design by using robust monotonic convergence (RMC) criteria. However, RMC leads to fundamental performance limitations. We consider the possibility of allowing safe transient growth in ILC algorithms as a means to circumvent these limitations. Here the pseudospectra is used for the first time to study transient growth in ILC. Basic properties of the pseudospectra that are relevant to the ILC problem are presented. Two ILC design problems are considered and examined using pseduospectra. The pseudospectra provides new results …

Approximating Stationary Statistical Properties, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. the main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. the result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are …

A Comparison Of Balanced Truncation Methods For Closed Loop Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

Real-time control of a physical system necessitates controllers that are low order. In this paper, we compare two balanced truncation methods as a means of designing low order compensators for partial differential equation (PDE) systems. The first method is the application of balanced truncation to the compensator dynamics, rather than the state dynamics, as was done in cite{Skelton:1984}. The second method, LQG balanced truncation, applies the balancing technique to the Riccati operators obtained from a specific LQG design. We discuss snapshot-based algorithms for constructing the reduced order compensators and present numerical results for a two dimensional convection diffusion PDE system.

Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs.

The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent …

A Snapshot Algorithm For Linear Feedback Flow Control Design, Benjamin T. Dickinson, Belinda A. Batten, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The control of fluid flows has many applications. For micro air vehicles, integrated flow control designs could enhance flight stability by mitigating the effect of destabilizing air flows in their low Reynolds number regimes. However, computing model based feedback control designs can be challenging due to high dimensional discretized flow models. In this work, we investigate the use of a snapshot algorithm proposed in Ref. 1 to approximate the feedback gain operator for a linear incompressible unsteady flow problem on a bounded domain. The main component of the algorithm is obtaining solution snapshots of certain linear flow problems. Numerical results …

A Proper Orthogonal Decomposition Approach To Approximate Balanced Truncation Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

We extend a method for approximate balanced reduced order model derivation for finite dimensional linear systems developed by Rowley (Int. J. Bifur. Chaos Appl. Sci. Eng. 15(3) (2005), pp. 997-1013) to infinite dimensional systems. The algorithm is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method can be also applied to nonlinear systems. Numerical results are presented for a convection diffusion system.

Effect Of Dlk1 And Rtl1 But Not Meg3 Or Meg8 On Muscle Gene Expression In Callipyge Lambs, Jolena N. Fleming-Waddell, Gayla R. Olbricht, Tasia M. Taxis, Jason D. White, Tony Vuocolo, Bruce A. Craig, Ross L. Tellam, Mike K. Neary, Noelle E. Cockett, Christopher A. Bidwell

Mathematics and Statistics Faculty Research & Creative Works

Callipyge sheep exhibit extreme postnatal muscle hypertrophy in the loin and hindquarters as a result of a single nucleotide polymorphism (SNP) in the imprinted DLK1-DIO3 domain on ovine chromosome 18. The callipyge SNP up-regulates the expression of surrounding transcripts when inherited in cis without altering their allele-specific imprinting status. The callipyge phenotype exhibits polar overdominant inheritance since only paternal heterozygous animals have muscle hypertrophy. Two studies were conducted profiling gene expression in lamb muscles to determine the down-stream effects of over-expression of paternal allele-specific DLK1 and RTL1 as well as maternal allele-specific MEG3, RTL1AS and MEG8, using Affymetrix bovine expression …

A Finite Element Splitting Extrapolation For Second Order Hyperbolic Equations, Xiaoming He, Tao Lü

Mathematics and Statistics Faculty Research & Creative Works

Splitting extrapolation is an efficient technique for solving large scale scientific and engineering problems in parallel. This article discusses a finite element splitting extrapolation for second order hyperbolic equations with time-dependent coefficients. This method possesses a higher degree of parallelism, less computational complexity, and more flexibility than Richardson extrapolation while achieving the same accuracy. By means of domain decomposition and isoparametric mapping, some grid parameters are chosen according to the problem. The multiparameter asymptotic expansion of the d-quadratic finite element error is also established. The splitting extrapolation formulas are developed from this expansion. An approximation with higher accuracy on a …