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Full-Text Articles in Control Theory

Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman Oct 2019

Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman

J. J. P. Veerman

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …


Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra Oct 2019

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Controllability And Observability Of Time-Varying Linear Nabla Fractional Systems, Tilekbek Zhoroev Oct 2019

Controllability And Observability Of Time-Varying Linear Nabla Fractional Systems, Tilekbek Zhoroev

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Relaxation And Linear Programs On A Hybrid Control Model, Héctor Jasso-Fuentes, Jose-Luis Menaldi Sep 2019

Relaxation And Linear Programs On A Hybrid Control Model, Héctor Jasso-Fuentes, Jose-Luis Menaldi

Mathematics Faculty Research Publications

Some optimality results for hybrid control problems are presented. The hybrid model under study consists of two subdynamics, one of a standard type governed by an ordinary differential equation, and the other of a special type having a discrete evolution. We focus on the case when the interaction between the subdynamics takes place only when the state of the system reaches a given fixed region of the state space. The controller is able to apply two controls, each applied to one of the two subdynamics, whereas the state follows a composite evolution, of continuous type and discrete type. By the ...


Some Recent Developments On Pareto-Optimal Reinsurance, Wenjun Jiang Jul 2019

Some Recent Developments On Pareto-Optimal Reinsurance, Wenjun Jiang

Electronic Thesis and Dissertation Repository

This thesis focuses on developing Pareto-optimal reinsurance policy which considers the interests of both the insurer and the reinsurer. The optimal insurance/reinsurance design has been extensively studied in actuarial science literature, while in early years most studies were concentrated on optimizing the insurer’s interests. However, as early as 1960s, Borch argued that “an agreement which is quite attractive to one party may not be acceptable to its counterparty” and he pioneered the study on “fair” risk sharing between the insurer and the reinsurer. Quite recently, the question of how to strike a balance in risk sharing between an ...


Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku May 2019

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.


Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu May 2019

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 ...


Traffic Signal Consensus Control, Gerardo Lafferriere Apr 2019

Traffic Signal Consensus Control, Gerardo Lafferriere

TREC Final Reports

We introduce a model for traffic signal management based on network consensus control principles. The underlying principle in a consensus approach is that traffic signal cycles are adjusted in a distributed way so as to achieve desirable ratios of queue lengths throughout the street network. This approach tends to reduce traffic congestion due to queue saturation at any particular city block and it appears less susceptible to congestion due to unexpected traffic loads on the street grid. We developed simulation tools based on the MATLAB computing environment to analyze the use of the mathematical consensus approach to manage the signal ...


A Decentralized Network Consensus Control Approach For Urban Traffic Signal Optimization, Gerardo Lafferriere Apr 2019

A Decentralized Network Consensus Control Approach For Urban Traffic Signal Optimization, Gerardo Lafferriere

TREC Project Briefs

Automobile traffic congestion in urban areas is a worsening problem that comes with significant economic and social costs. This report offers a new approach to urban congestion management through traffic signal control.


Condensed Forms For Linear Port-Hamiltonian Descriptor Systems, Lena Scholz Mar 2019

Condensed Forms For Linear Port-Hamiltonian Descriptor Systems, Lena Scholz

Electronic Journal of Linear Algebra

Motivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs) are derived. Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow for the further analysis of the properties of port-Hamiltonian DAEs and to study, e.g., existence and uniqueness of solutions or to determine the index. It can be shown that under certain conditions for regular port-Hamiltonian DAEs the strangeness index is bounded by $\mu\leq1$.


Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, Jessica S. Lugo Jan 2019

Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, Jessica S. Lugo

Murray State Theses and Dissertations

Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules.

The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost ...


Long-Run Average Cost Minimization Of A Stochastic Processing System, Bowen Xie Jan 2019

Long-Run Average Cost Minimization Of A Stochastic Processing System, Bowen Xie

Creative Components

A long-run average cost problem in stochastic control theory is addressed. This problem is related to the optimal control of a production-inventory system which is subjected to random fluctuation. The approach taken here is based on finding a smooth solution to the corresponding Hamilton-Jacobi-Bellman equation. This solution in turn is used to derive an optimal process for the above long-run average cost problem. Using the invariant distributions for positive recurrent diffusion processes, another derivation for the optimal long-run average cost is provided here.


Stabilize Chaotic Flows In A Coupled Triple-Loop Thermosyphon System, Haley N. Anderson Jan 2019

Stabilize Chaotic Flows In A Coupled Triple-Loop Thermosyphon System, Haley N. Anderson

University Honors Program Theses

This study addresses the control of chaotic dynamic systems represented by three coupled Lorenz systems. In application, Lorenz systems are commonly used to describe the one-dimensional motion of fluids in a tube when heated below and cooled above. This system, in particular, reflects the fluid motion in a coupled triple-loop thermosyphon system. The goal is to derive a system of nonlinear differential equations to help us study various flow patterns governed by such a high-dimensional nonlinear model numerically. Once the driving parameter (Rayleigh number) values are identified corresponding to the chaotic regime, a minimal number of proportional controllers are designed ...


Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman Jan 2019

Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to ...


Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski Dec 2018

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Discontinuity Propagation In Delay Differential-Algebraic Equations, Benjamin Unger Dec 2018

Discontinuity Propagation In Delay Differential-Algebraic Equations, Benjamin Unger

Electronic Journal of Linear Algebra

The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencils, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as a worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE and allows to study exponential stability of the DDAE based on the spectral abscissa. The new classification ...


Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright Dec 2018

Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

Mathematics & Statistics ETDs

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to ...


Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma Nov 2018

Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma

Electronic Journal of Linear Algebra

Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and symmetry-structure-preserving perturbations. It is shown that these eigenvalue and eigenpair backward errors are sometimes significantly larger than the corresponding backward errors that are obtained under perturbations that ignore the special structure of the pencil.


Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, Ahmet Ozkan Ozer, Emma J. Moore Nov 2018

Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, Ahmet Ozkan Ozer, Emma J. Moore

Posters-at-the-Capitol

Piezoelectric materials have the unique ability to convert electrical energy to mechanical vibrations and vice versa. This project takes a stab to develop a reliable computational tool to simulate the vibration control of a novel “partial differential equation” model for a piezoelectric device, which is designed by integrating electric conducting piezoelectric layers constraining a viscoelastic layer to provide an active and lightweight intelligent structure. Controlling unwanted vibrations on piezoelectric devices (or harvesting energy from ambient vibrations) through piezoelectric layers has been the major focus in cutting-edge engineering applications such as ultrasonic welders and inchworms. The corresponding mathematical models for piezoelectric ...


Using Canalization For The Control Of Discrete Networks, David Murrugarra Oct 2018

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Identifying Combinatorially Symmetric Hidden Markov Models, Daniel Burgarth Aug 2018

Identifying Combinatorially Symmetric Hidden Markov Models, Daniel Burgarth

Electronic Journal of Linear Algebra

A sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models, based on the structure of their transition matrix, is provided. If the observed states of the chain form a zero forcing set of the graph of the Markov model, then it is uniquely identifiable and an explicit reconstruction method is given.


On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, Jessie Jamieson Aug 2018

On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, Jessie Jamieson

Dissertations, Theses, and Student Research Papers in Mathematics

The theory of beams and plates has been long established due to works spanning many fields, and has been explored through many investigations of beam and plate mechanics, controls, stability, and the well-posedness of systems of equations governing the motions of plates and beams. Additionally, recent investigations of flutter phenomena by Dowell, Webster et al. have reignited interest into the mechanics and stability of nonlinear beams. In this thesis, we wish to revisit the seminal well-posedness results of Lagnese and Leugering for the one dimensional, nonlinear beam from their 1991 paper, "Uniform stabilization of a nonlinear beam by nonlinear boundary ...


On Some Ergodic Impulse Control Problems With Constraint, J. L. Menaldi, Maurice Robin Jul 2018

On Some Ergodic Impulse Control Problems With Constraint, J. L. Menaldi, Maurice Robin

Mathematics Faculty Research Publications

This paper studies the impulse control of a general Markov process under the average (or ergodic) cost when the impulse instants are restricted to be the arrival times of an exogenous process, and this restriction is referred to as a constraint. A detailed setting is described, a characterization of the optimal cost is obtained as a solution of an HJB equation, and an optimal impulse control is identified.


Curve Tracking Control Under State Constraints And Uncertainties, Robert Kelly Sizemore Jul 2018

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 ...


Backstepping And Sequential Predictors For Control Systems, Jerome Avery Weston Jun 2018

Backstepping And Sequential Predictors For Control Systems, Jerome Avery Weston

LSU Doctoral Dissertations

We provide new methods in mathematical control theory for two significant classes of control systems with time delays, based on backstepping and sequential prediction. Our bounded backstepping results ensure global asymptotic stability for partially linear systems with an arbitrarily large number of integrators. We also build sequential predictors for time-varying linear systems with time-varying delays in the control, sampling in the control, and time-varying measurement delays. Our bounded backstepping results are novel because of their use of converging-input-converging-state conditions, which make it possible to solve feedback stabilization problems under input delays and under boundedness conditions on the feedback control. Our ...


Discrete-Time Hybrid Control In Borel Spaces, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau May 2018

Discrete-Time Hybrid Control In Borel Spaces, Héctor Jasso-Fuentes, José-Luis Menaldi, Tomás Prieto-Rumeau

Mathematics Faculty Research Publications

A discrete-time hybrid control model with Borel state and action spaces is introduced. In this type of models, the dynamic of the system is composed by two sub-dynamics affecting the evolution of the state; one is of a standard-type that runs almost every time and another is of a special-type that is active under special circumstances. The controller is able to use two different type of actions, each of them is applied to each of the two sub-dynamics, and the activations of these sub-dynamics are possible according to an activation rule that can be handled by the controller. The aim ...


Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni Apr 2018

Near-Optimal Control Of Switched Systems With Continuous-Time Dynamics Using Approximate Dynamic Programming, Tohid Sardarmehni

Mechanical Engineering Research Theses and Dissertations

Optimal control is a control method which provides inputs that minimize a performance index subject to state or input constraints [58]. The existing solutions for finding the exact optimal control solution such as Pontryagin’s minimum principle and dynamic programming suffer from curse of dimensionality in high order dynamical systems. One remedy for this problem is finding near optimal solution instead of the exact optimal solution to avoid curse of dimensionality [31]. A method for finding the approximate optimal solution is through Approximate Dynamic Programming (ADP) methods which are discussed in the subsequent chapters.

In this dissertation, optimal switching in ...


Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle Apr 2018

Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle

Master's Theses and Project Reports

This thesis is intended to provide fundamental information for the construction and

analysis of rotordynamic theoretical models, and their comparison the experimental

systems. Finite Element Method (FEM) is used to construct models using Timoshenko

beam elements with viscous and hysteretic internal damping. Eigenvalues

and eigenvectors of state space equations are used to perform stability analysis, produce

critical speed maps, and visualize mode shapes. Frequency domain analysis

of theoretical models is used to provide Bode diagrams and in experimental data

full spectrum cascade plots. Experimental and theoretical model analyses are used

to optimize the control algorithm for an Active Magnetic Bearing ...


Controllability And Observability Of The Discrete Fractional Linear State-Space Model, Duc M. Nguyen Apr 2018

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, Dina Alina Irofti, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu Feb 2018

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 ...