Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, 2019 Laboratoire des Signaux et Syst`emes (L2S) CentraleSup´elec-CNRS-Universit´e Paris Sud, 3 rue Joliot- Curie 91192 Gif-sur-Yvette cedex, France.

#### Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

*SIUE Faculty Research, Scholarship, and Creative Activity*

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the ...

Curve Tracking Control Under State Constraints And Uncertainties, 2018 Louisiana State University

#### Curve Tracking Control Under State Constraints And Uncertainties, Robert Kelly Sizemore

*LSU Doctoral Dissertations*

We study a class of steering control problems for free-moving particles tracking a curve in the plane and also in a three-dimensional environment, which are central problems in robotics. In the two-dimensional case, we provide adaptive controllers for curve tracking under unknown curvatures and control uncertainty. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature to form the augmented error dynamics. This nonlinear dependence puts our curvature identification objective outside the scope of existing adaptive tracking and parameter identification results that were limited to cases where the unknown parameters ...

Controllability And Observability Of The Discrete Fractional Linear State-Space Model, 2018 Western Kentucky University

#### Controllability And Observability Of The Discrete Fractional Linear State-Space Model, Duc M. Nguyen

*Masters Theses & Specialist Projects*

This thesis aims to investigate the *controllability *and *observability *of the discrete fractional linear time-invariant state-space model. First, we will establish key concepts and properties which are the tools necessary for our task. In the third chapter, we will discuss the discrete state-space model and set up the criteria for these two properties. Then, in the fourth chapter, we will attempt to apply these criteria to the discrete fractional model. The general flow of our objectives is as follows: we start with the first-order linear difference equation, move on to the discrete system, then the fractional difference equation, and finally ...

Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, 2018 Laboratoire des Signaux et Systèmes (L2S) CNRS-CentraleSupélec-Université Paris-Sud, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France

#### Some Insights Into The Migration Of Double Imaginary Roots Under Small Deviation Of Two Parameters, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

*SIUE Faculty Research, Scholarship, and Creative Activity*

This paper studies the migration of double imaginary roots of the systems’ characteristic equation when two parameters are subjected to small deviations. The proposed approach covers a wide range of models. Under the least degeneracy assumptions, we found that the local stability crossing curve has a cusp at the point that corresponds to the double root, and it divides the neighborhood of this point into an S-sector and a G-sector. When the parameters move into the G-sector, one of the roots moves to the right halfplane, and the other moves to the left half-plane. When the parameters move into the ...

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, 2018 Nanjing University of Science and Technology

#### Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

*SIUE Faculty Research, Scholarship, and Creative Activity*

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between local strong ...

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, 2018 School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China

#### Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

*SIUE Faculty Research, Scholarship, and Creative Activity*

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between local strong stability, the ...

Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, 2018 The University of Akron

#### Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, Mackenzie Jones

*Honors Research Projects*

In Dunn County, Wisconsin the lakes suffer from algae blooms due to excess phosphorus runoff. A coupled bio-economic model is studied with the intent of finding the optimal level of phosphorus that should be allowed into the lake depending on certain biologic and economic parameters. We model the algae and phosphorus concentration in the lake over time based off the phosphorus input. Community welfare is modeled by comparing the costs and benefits of phosphorus fertilizer. This model is proposed to find the phosphorus level that maximizes community welfare and then determine how certain environmental and social change initiatives will affect ...

Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, 2017 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

The General $\Phi$-Hermitian Solution To Mixed Pairs Of Quaternion Matrix Sylvester Equations, 2017 Auburn University

#### The General $\Phi$-Hermitian Solution To Mixed Pairs Of Quaternion Matrix Sylvester Equations, Zhuo-Heng He, Jianzhen Liu, Tin-Yau Tam

*Electronic Journal of Linear Algebra*

Let $\mathbb{H}^{m\times n}$ be the space of $m\times n$ matrices over $\mathbb{H}$, where $\mathbb{H}$ is the real quaternion algebra. Let $A_{\phi}$ be the $n\times m$ matrix obtained by applying $\phi$ entrywise to the transposed matrix $A^{T}$, where $A\in\mathbb{H}^{m\times n}$ and $\phi$ is a nonstandard involution of $\mathbb{H}$. In this paper, some properties of the Moore-Penrose inverse of the quaternion matrix $A_{\phi}$ are given. Two systems of mixed pairs of quaternion matrix Sylvester equations $A_{1}X-YB_{1}=C_{1},~A_{2}Z-YB_{2}=C_ ...

Rogue Rotary - Modular Robotic Rotary Joint Design, 2017 California Polytechnic State University, San Luis Obispo

#### Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

*Mechanical Engineering*

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.

Social Balance And The Bernoulli Equation, 2017 Portland State University

#### Social Balance And The Bernoulli Equation, J. J. P. Veerman

*Mathematics and Statistics Faculty Publications and Presentations*

Since the 1940s there has been an interest in the question of why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This note provides an introduction to the notion of social balance and a new (and simplified) analysis of that model. This new analysis allows us to choose general initial conditions, as opposed to the symmetric ones previously considered. We show that for general initial conditions, four factions will evolve instead of two. We characterize the four factions, and give an idea of their ...

Mathematical Studies Of Optimal Economic Growth Model With Monetary Policy, 2017 College of William and Mary

#### Mathematical Studies Of Optimal Economic Growth Model With Monetary Policy, Xiang Liu

*Undergraduate Honors Theses*

In this paper, efforts will be made to study an extended Neoclassic economic growth model derived from Solow-Swan Model and Ramsey-Cass-Koopsman Model. Some growth models (e.g. Solow-Swan Model) attempt to explain long-run economic growth by looking at capital accumulation, labor or population growth, and in- creases in productivity, while our derived model tends to look at growth from individual household and how their choice of saving, consumption and money holdings would affect the overall economic capital accumulation over a long period of time.

First an optimal control model is set up, and a system of differential equations and algebraic ...

Optimal Control And Models For Alternative Pest Management To Alfalfa Agroecosystems, 2017 Hartnell College

#### Optimal Control And Models For Alternative Pest Management To Alfalfa Agroecosystems, Mohammed Yahdi

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Data Predictive Control Using Regression Trees And Ensemble Learning, 2017 University of Pennsylvania

#### Data Predictive Control Using Regression Trees And Ensemble Learning, Achin Jain, Francesco Smarra, Rahul Mangharam

*Real-Time and Embedded Systems Lab (mLAB)*

Decisions on how to best operate large complex plants such as natural gas processing, oil refineries, and energy efficient buildings are becoming ever so complex that model-based predictive control (MPC) algorithms must play an important role. However, a key factor prohibiting the widespread adoption of MPC, is the cost, time, and effort associated with learning first-principles dynamical models of the underlying physical system. An alternative approach is to employ learning algorithms to build black-box models which rely only on real-time data from the sensors. Machine learning is widely used for regression and classification, but thus far data-driven models have not ...

A Study Of The Reduction Of Excessive Energy Generated By Strong Winds On Power Lines Via A Velocity Damping Controller At The Transmission Tower, 2017 Kent State University - Kent Campus

#### A Study Of The Reduction Of Excessive Energy Generated By Strong Winds On Power Lines Via A Velocity Damping Controller At The Transmission Tower, Donald W. Fincher Jr.

*Undergraduate Research Symposium*

In this research, we are pursuing the robustness of a self-excited vibrational system with negative damping. In practice, this is manifested as conductor galloping of overhead power lines, which is an oscillation of the lines caused by strong winds. Improved transmission tower designs are needed which are capable of combating excessive stresses exerted on the tower by the galloping power lines. Our model of this self-excited system shows that the oscillations can be controlled by adding a boundary velocity feedback controller at the transmission tower. Using a decomposition method, we show there is a closed form analytical solution which predicts ...

P26. Global Exponential Stabilization On So(3), 2017 sberkane@uwo.ca

#### P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

*Western Research Forum*

Global Exponential Stabilization on SO(3)

Carrying Asymmetric Loads During Stair Negotiation, 2017 Iowa State University

#### Carrying Asymmetric Loads During Stair Negotiation, Junsig Wang, Jason C. Gillette

*Kinesiology Publications*

Individuals often carry items in one hand instead of both hands during activities of daily living. The combined effects of carrying asymmetric loads and stair negotiation may create even higher demands on the low back and lower extremity. The purpose of this study was to investigate the effect of symmetric and asymmetric loading conditions on L5/S1 and lower extremity moments during stair negotiation. Twenty-two college students performed stair ascent and stair descent on a three-step staircase (step height 18.5 cm, tread depth 29.5 cm) at preferred pace under five load conditions: no load, 10% body weight (BW ...

Data Predictive Control For Building Energy Management, 2017 University of Pennsylvania

#### Data Predictive Control For Building Energy Management, Achin Jain, Madhur Behl, Rahul Mangharam

*Real-Time and Embedded Systems Lab (mLAB)*

Decisions on how to best optimize energy systems operations are becoming ever so complex and conflicting, that model-based predictive control (MPC) algorithms must play an important role. However, a key factor prohibiting the widespread adoption of MPC in buildings, is the cost, time, and effort associated with learning first-principles based dynamical models of the underlying physical system. This paper introduces an alternative approach for implementing finite-time receding horizon control using control-oriented data-driven models. We call this approach Data Predictive Control (DPC). Specifically, by utilizing separation of variables, two novel algorithms for implementing DPC using a single regression tree and with ...

On Some Impulse Control Problems With Constraint, 2017 Wayne State University

#### On Some Impulse Control Problems With Constraint, Jose L. Menaldi, Maurice Robin

*Mathematics Faculty Research Publications*

The impulse control of a Markov–Feller process is considered when the impulses are allowed only when a signal arrives. This is referred to as an impulse control problem with constraint. A detailed setting is described, a characterization of the optimal cost is obtained using previous results of the authors on optimal stopping problems with constraint, and an optimal impulse control is identified.

C.V. - Wojciech Budzianowski, 2017 Wojciech Budzianowski Consulting Services