Dylan R. S. Poulsen, Ph.D.

Mathematician, Writer, Educator, Consultant

## Research Interests

Dynamic Equations on Time Scales, Linear Systems, Control Theory, Stochastic Processes, Matrix Equations

## Education

`2010-2015`

**Baylor University,** Waco, TX

Ph.D. Mathematics, May 2015

- Thesis Title: Stability and Control on Stochastically Generated Time Scales
- Advisor: John M. Davis, Ph.D

`2006-2010`

**University of Puget Sound**, Tacoma, WA

B.S., Mathematics, May 2010

- Summa Cum Laude
- Phi Beta Kappa

## Publications

### Journal articles

- Tom Cuchta,
**Dylan Poulsen**, and Nick Wintz “Linear Quadratic Tracking and Continuous Conformable Derivatives”*European Journal of Control.*To appear. - Billy J. Jackson, John M. Davis, and
**Dylan Poulsen**“A Polar Representation of the Hilger Complex Plane”*International Journal of Difference Equations***15**: (2020) 419 - 427. **Dylan Poulsen**, Michael Defoort, and Mohamed Djemai “Mean Square Consensus of Double-Integrator Multi-Agent Systems Under Intermittent Control: A Stochastic Time Scale Approach”*Journal of the Franklin Institute***356**: (2019) 9076 - 9094.**Dylan Poulsen**and Nick Wintz. “The Kalman Filter on Stochastic Time Scales.”*Nonlinear Analysis: Hybrid Systems***33**(2019): 151-161.**Dylan Poulsen**, John M. Davis, and Ian A. Gravagne. “Mean Square Stabilityfor Systems on Stochastically Generated Discrete Time Scales.”*Nonlinear Analysis: Hybrid Systems***31**(2019): 41-55.**Dylan Poulsen**, John M. Davis, and Ian A. Gravagne. “The Geometry of the Region of Uniform Exponential Stability for Linear Time Invariant Dynamic Equations on Time Scales.”*DCDIS Series A: Mathematical Analysis***25**(2018): 159-173.

### Peer-Reviewed Conference Publications

**Dylan Poulsen**, Michael Defoort, and Mohamed Djemai. “Observer-Based Output Feedback Consensus Protocol for Double-Integrator Multi-Agent Systems Under Intermittent Sampled Position Measurements.”*IFAC-PapersOnLine*. IFAC, 2020.**Dylan Poulsen**, John M. Davis, and Ian A. Gravagne. “Optimal Control on Stochastic Time Scales.”*IFAC-PapersOnLine*. IFAC, 2017.**Dylan Poulsen**, Shaun Ramsey, and Nathaniel Schwartz. “The Emergence of Chaos on Non-Uniformly Timed Systems.”*2017 51st Annual Conference on Information Sciences and Systems (CISS)*. IEEE, 2017.**Dylan Poulsen**, Ian A. Gravagne, and John M. Davis. “Numeric and Analytic Investigations of Mean-Square Exponential Stability for Stochastically Timed Systems.”*2015 Dynamic Systems and Control Conference*. ASME, 2015.- Matthew Mosley, Ian A. Gravagne, John M. Davis, and
**Dylan Poulsen**. “ Experimental Investigation of a Time Scales-Based Stability Criterion Over Finite Time Horizons.” 2015 Dynamic Systems and Control Conference. ASME, 2015. **Dylan Poulsen**, John M. Davis, and Ian A. Gravagne. “Is Deterministic Real Time Control Always Necessary? A Time Scales Perspective.”*2014 Dynamic Systems and Control Conference.*ASME, 2014.**Dylan Poulsen**, John M. Davis, and Ian A. Gravagne. “Observer based feedback controllers on stochastic time scales.”*2013 45th Southeastern Symposium on System Theory (SSST).*IEEE, 2013.**Dylan Poulsen**, John M. Davis, and Ian A. Gravagne. “Stochastic time scales: quadratic Lyapunov functions and probabilistic regions of stability.”*2013 45th Southeastern Symposium on System Theory (SSST).*IEEE, 2013.- Ian A. Gravagne, John M. Davis, and
**Dylan Poulsen**. “Time scale-based observer design for battery state-of-charge estimation.”*2012 44th Southeastern Symposium on System Theory (SSST).*IEEE, 2012. **Dylan Poulsen**, Ian A. Gravagne, John M. Davis, and Robert J. Marks. “On the stability of mu-varying dynamic equations on stochastically generated time scales.”*2012 44th Southeastern Symposium on System Theory (SSST).*IEEE, 2012.**Dylan Poulsen**, Michael Z. Spivey, and Robert J. Marks. “The Poisson Process and Associated Probability Distributions on Time Scales.”*2011 43rd Southeastern Symposium on System Theory (SSST).*IEEE, 2011.

## Institutional Grants

`Summer 2020`

*Lowering the Barrier to Entry in Probability via Coding and Simulation Labs,*Cromwell Center for Teaching and Learning Innovative Pedagogy Grant, Funded, $2000.`Summer 2018`

*The Application of Stochastic Time Scales to Control Engineering,*Faculty Enhancement Grant, Funded, $1,008.`Spring 2017`

*Differential Calculus,*Cromwell Center for Teaching and Learning Innovative Pedagogy Grant, Funded, $5,000 (Co-PI with Nathaniel Schwartz)

## Presentations

### Invited Colloquim Speaker

`Jan 2022`

Christopher Newport University Department of Mathematics Colloquium. “Finding Mathematical Joy Cutting Onions.”`June 2018`

University of Valenciennes Séminaire ROC du Département Auto. “Stability of Linear Systems Subject to Stochastic Timing.”`Mar 2018`

United States Naval Academy Applied Mathematics Seminar. “Engineering in an Imperfect World.”`Sept 2016`

Christopher Newport University Department of Mathematics Colloquium. “Engineering in an Imperfect World.”

### Conference Speaker

`July 2020`

IFAC World Congress, Berlin, Germany (Virtual). “Observer-Based Output Feedback Consensus Protocol for Double-Integrator Multi-Agent Systems Under Intermittent Sampled Position Measurements.”`Jan 2019`

Joint Mathematics Meetings, Baltimore, MD. “Consensus of Multi-Agent Systems: A Time Scales Approach.”`July 2017`

IFAC World Congress, Toulouse, France July 2017. “Opitmal Control on Stochastic Time Scales.”`Jan 2016`

Joint Mathematics Meetings, Seattle, WA. “Can an Unstable Control System Be Stabilized By Timing Noise?”`Nov 2015`

MAA MD-DC-VA Sectional Meeting, Saint Marys City, MD. “Can an Unstable Control System Be Stabilized By Timing Noise?”`Oct 2015`

ASME 2015 Dynamic Systems and Control Conference, Columbus, OH. “Numeric and Analytic Investigations of Mean-Square Exponential Stability for Stochastically Timed Systems.”`Jan 2015`

Joint Mathematics Meetings, San Antonio, TX. “The Geometry of the Region of Uniform Exponential Stability on an Arbitrary Time Scale.”`Oct 2014`

ASME 2014 Dynamic Systems and Control Conference, San Antonio, TX. “Is Deterministic Real Time Control Always Necessary? A Time Scales Perspective.”`Jan 2014`

Joint Mathematics Meetings, Baltimore, MD. “Stability of Markov Chains: A Time Scales Viewpoint with Applications to Control.”`Oct 2013`

Central Section Fall Meeting of the AMS, St. Louis, MO. “Stability of Markov Chains: A Time Scales Viewpoint with Applications to Control.”`Mar 2013`

Southeastern Symposium on Systems Theory, Waco, TX.- “Stochastic Time Scales: Quadratic Lyapunov Functions and Probabilistic Regions of Stability.”
- “Observer Based Feedback Controllers on Stochastic Time Scales.”

`Mar 2012`

Southeastern Symposium on Systems Theory, Jacksonville, FL.- “On the Stability of Mu-Varying Dynamic Equations on Stochastically Generated Time Scales.”
- “Time Scale-Based Observer Design for Battery State-of-Charge Estimation.”

`Mar 2011`

Southeastern Symposium on Systems Theory, Auburn, AL. “The Poisson Process and Associated Probability Distributions on Time Scales.”`Oct 2009`

Central Section Fall Meeting of the AMS, Waco, TX. “Coupled Conditions for Asymptotic Equivalence on Time Scales.”`Oct 2009`

INFORMS Annual National Meeting, San Diego, CA. “The Optimal Tilt Angle of Solar Panels.”`Aug 2009`

MAA MathFest, Portland, OR. “The Optimal Tilt Angle of Solar Panels.”`June 2009`

Rocky Mountain Mathematics Consortium, Laramie, WY. “Coupled Conditions for Asymptotic Equivalence on Time Scales.”`Apr 2009`

MAA Paciffic Northwest Sectional Meeting, Ellensburg, WA. “The Asymptotic Behavior of Dynamic Equations on Time Scales.”

### Conference Poster Presentations

`Mar 2019`

American Association for Cancer Research Annual Meeting 2019. “Rapid Fluorescence Based Assessment of RNA Integrity Quality Using Machine Learning.” Presented by Scott Clarke.

## Teaching Experience

`2021-`

**Washington College** Associate Professor of Mathematics

`2015-21`

**Washington College** Assistant Professor of Mathematics

### Courses Designed and Managed at Washington College

`Two Sections`

MAT 109 - Statistics`Ten Sections`

MAT 111 - Differential Calculus`Twelve Sections`

MAT 112 - Integral Calculus`One Section`

MAT 199 - History of Mathematics`Two Sections`

MAT 210 - Multivariable Calculus`Seven Sections`

MAT 280 - Linear Algebra`Four Sections`

MAT 310 - Differential Equations`Two Sections`

MAT 320 - Probability Theory`One Section`

MAT 392 and 492 - Junior and Senior Math Seminar`Three Sections`

MAT 470 - Real Analysis

### Senior Capstone Projects Mentored at Washington College

`2022-2023`

Sneha Dixit “The Fourier Transform and Applications.” In Progress`2022-2023`

Seyed Marjaei “Propeller Design and Dynamic Mode Decomposition.” In Progress`2022`

Rachel Chatfield “Mathematical Scaling and Use of Organ-on-a-Chip for Disease Modeling and Drug Testing.”`2022`

Sam Hickman “LQR Control of a Reaction Wheel Inverted Pendulum.”`2021-2022`

Evan McCarthy “Power System Automation for Electric Race Boats.”`2021-2022`

Chloe Sass “The Discrete Kalman Filter.”`2021-2022`

Kennett Vail-Rojas “On the Interactions of Black Holes and Dark Matter: Primordial Black Holes as Potential Dark Matter Constituents.”`2020-2021`

Brendan Farrell “A Review of Superconductivity.”`2019-2020`

Nicole Albrecht “An Introduction To Compartmental Models Of Infectious Disease.”`2019-2020`

Patrick Berry “Quantum Computing.”`2019`

Gauge Burnett “Fantastic Knots and How to Tie Them.”`2018-2019`

Simon Checknoff “Using Lie Symmetries to Solve Differential Equations.”`2018-2019`

Molly Flowers “ An Experimental Study of Time-Reversal Acoustics.”`2018-2019`

Kevin McCormick “Optimal Control Theory: Dynamic Programming of Solar Panel Consumption.”`2018-2019`

Sheng Mi “Brownian Motion and Stock Prices”`2017-2018`

Yilin Yang “The Application of Mathematics in the Game ‘Lights Out.’”`2017-2018`

Alexandra Young “Female Labor Force Participation Rate Effects on Births”`2017-2018`

Courtney Rainey “Exploding Dots and Division Rules.”`2016-2017`

Dimitri Kaliakin “Assessment of Kellers Mathematical Model for Optimal Velocity in a Footrace”`2016-2017`

Ricardo Wu “Model of Business Risk Management.”`2015-2016`

Bryten Ives “Theory and Actuarial Applications of Stochastic Processes.”`2015-2016`

Maisie Newman “Efficiently Modeling the Control of West Nile Virus.”`2015-2016`

Laurel Jones “Exploring Mathematical Models of the Bacterium*Clostridium difficile*.”

`2011-2015`

**Baylor University** Teacher of Record, Department of Mathematics

### Courses Managed at Baylor University

`Three Sections`

MTH 1320 - Precalculus Mathematics`One Section`

MTH 1321 - Calculus I`One Section`

MTH 1308 - Precalculus for Business Students`One Section`

MTH 1309 - Calculus for Business Students

### Mentor for Undergraduate Research At Baylor University

`Spring 2013`

Brooklyn George “On the Stability Region for Dynamic Equations on the Cantor Set.”`2014-2015`

Matthew Mosely “ Applications of Dynamic Equations on Time Scales.” Honors Thesis on Engineering

## Honors

### Teaching Awards

`May 2015`

Baylor University Department of Mathematics Outstanding Graduate Student Teaching Award.`Jan 2023`

Cromwell Award for Innovation in Teaching, Cromwell Center for Teaching and Learning, Washington College.

### Professional Development Fellowships

`June 2015 - August 2016`

Project NExT Fellow. Project NExT is a professional development program for early-career mathematicians.

## Honor Societies

`Fall 2015`

Pi Mu Epsilon, Iota of Maryland. Charter faculty member.`Spring 2010`

Phi Beta Kappa, Delta of Washington.

## Service to the Profession

### Chairing Sessions

- Joint Mathematics Meetings, Baltimore, MD Jan 2014. AMS Session on Game Theory and Computing.
- Joint Mathematics Meetings, San Antonio, TX Jan 2015. AMS Session on Game Theory, Economics, Control Theory, and Information.
- Joint Mathematics Meetings, Seattle, WA Jan 2016. AMS Session on Computer Science, Information, Control Theory, and Economics.

### Peer Review

*Nonlinear Analysis: Hybrid Systems*Four Reviews. Outstanding Reviewer Status.*Journal of the Franklin Institute*Two Reviews. Recognized Reviewer Status.*IFAC World Congress 2020*Two Reviews.*Advances in Difference Equations*One Review.

## Service to Washington College

`Fall 2021 - Present`

Chair, Department of Mathematics and Computer Science.`Fall 2021 - Present`

Member, Tenure and Promotion Committee.`Fall 2019 - Fall 2021`

Member, Assessment Committee.`Fall 2017 - Fall 2019`

Faculty Advisor to the Student Government Association.`Fall 2017 - Fall 2019`

Chair, Student Life Committee.`Fall 2016 - Spring 2018`

Member, Cromwell CTL Advisory Board.`2015, 2017, 2018, 2021`

Member, Search Committee for the Department of Mathematics and Computer Science.