Irena Lasiecka

Irena Lasiecka

Lasiecka's staff picture for the University of Virginia
Born February 4, 1948
Warsaw, Poland
Nationality Polish
Education University of Warsaw, Ph.D in Applied Mathematics, 1972
Occupation Mathematician and Professor of Mathematics
Years active 44
Known for Research in Applied Mathematics
Notable work

Applied Mathematics: Control Theory and Optimization Partial Differential Equations

Approximately 100 research papers published in major journals.
Board member of

American Mathematical Society International Federal Information Processes

Society of Industrial and Applied Mathematics
Awards

Silver Core Award

Polish Acadamy of Sciences Award

Irena Lasiecka (born February 4, 1948) is a Polish-American mathematician, a Distinguished University Professor of mathematics and chair of the mathematics department at the University of Memphis. She is also co-editor-in-chief of two academic journals, Applied Mathematics & Optimization and Evolution Equations & Control Theory.[1]


Lasiecka earned her Ph.D. in 1975 from the University of Warsaw under the supervision of Andrzej Wierzbicki.[2] In 2014, she became a fellow of the American Mathematical Society "for contributions to control theory of partial differential equations, mentorship, and service to professional societies."[3]

Her specific areas of study are partial differential equations and related control theory, Non-Linear PDEs, the optimization theory, calculus of variations, and boundary stabilization.

Early life and education

Irena was born and raised in Poland, where she received her initial background in mathematics. She studied math for many years at the University of Warsaw, where she earned her Master of Science degree in applied mathematics in 1972. A few years later, she received her PhD from the same university in the same field of study. [4]

Teaching

After receiving her PhD, Lasiecka started to transfer her knowledge of Applied Mathematics to others in addition to more personal studying and research. Her first teaching job was at the Polish Academy of Sciences in 1975, and she later ventured to the United States a few years later, teaching at the University of California, Los Angeles. She has been teaching in the US ever since. The following is a chart listing the institutions in which Lasiecka has been a teaching faculty member of. [4]

University Location of School Years There Area of University Status
Polish Academy of Sciences Warsaw, Poland 1975-1980 Control Theory Institute Assistant Professor
University of California, Los Angeles Los Angeles, CA 1977-1980 Systems Science Institute Postdoctoral Fellow 1977-1979; Visiting Assistant Professor, 1979-1980
University of Florida Gainesville, Florida 1980-1987 Mathematics Department Assistant Professor, 1980-1981; Associate Professor, 1981-1984; Professor, 1984-1987
University of Virginia Charlottesville, Virginia 1987-2011 Applied Mathematics and Mathematics departments Department of Applied Mathematics, Professor, 1987-1998; Department of Mathematics, Professor 1998-2011; Commonwealth Professor of Mathematics, 2011-present
University of Memphis Memphis, Tennessee 2013-present Mathematics Department, chair University distinguished professor
University of Warsaw, where Irena studied for many years.
University of Memphis, where Irena is currently teaching.

Areas of Study in Applied Mathematics

Optimization:

Optimization is the mathematical practice of finding the maximum or minimum values for a specific function. It has many real-world uses, and is a  common practice for people of many different professions. Economists and businessmen use this to maximize profit and minimize cost, a builder may use this to minimize the amount of materials for a given square feet of area, and a farmer may use this to maximize crop output. Common maximizations are areas, volumes, and profits, and common minimizations are distances, times, and costs.

Example of Optimization: A homeowner has 1600 feet of fencing and wants to fence off a rectangular yard that borders the house. There is no fence bordering the house. What are the dimensions of the house that has the largest area?

In this problem, we must find a length and width of the fencing that would produce the largest area. So, if “y” represents length and “x” represents width, we can assume that xy=A. However, since we only have a two widths, our equation must be:

2x+y=1600

It is much easier to solve this equation if it is in terms of one variable, so we can get rid of y by expressing it in terms of x. Therefore, y=-2x+1600. This we can now plug into A=xy.

xy=x(-2x+1600)

This equals -2x^2+1600x.

Next, take the derivative of this equation and find the critical numbers.

A’(x)=-4x+1600x

This will give a critical number of x=400

This means that the two widths (x)=400 feet of fencing and the length (y) is 800 feet of fencing, yielding a maximum area of 1200 feet. [5]

Lasiecka uses this same strategy to optimize differential systems, which is an equation that relates a function to its derivatives. She has written extensively about this topic in her collaborative work Contemporary Mathematics: Optimization Methods in Partial Differential Equations. [6]

Control theory

Control Theory is one of Irena Lasiecka's chief areas of study. She begins her book, Mathematical Control Theory of Coupled PDEs, with an description of what Control Theory is. She states, " The classical viewpoint taken in the study of differential equations consisted of the (passive) analysis of the evolution properties displayed by a specific equation, or a class of equations, in response to given data. Control theory, however, injects an active mode of synthesis in the study of differential equations: it seeks to influence their dynamical evolution by selecting and synthesizing suitable data (input functions or control functions) from within a preassigned class, to achieve a predetermined desired outcome or performance." [7]

In simpler terms, control theory is the ability to influence change in a system, something that changes over time. In order to better understand this concept, it is useful to know a few key phrases. A state is a representation of what the system is currently doing, dynamics is how the state changes, reference is what we want the system to do, an output is the measurements of the system, an input is a control signal, and feedback is the mapping from outputs to inputs. This can be applied to many facets of real-life, especially in various engineering fields that concentrate on the control of changes in their field. A good example of control theory applied to the real world is something as simple as a thermostat. The output in this system is temperature, and the control is turning the dial on or off, or to a higher or lower temperature. [8]

Irena uses this theory to further understand Partial differential equations. She attempts to answer the questions of how to take advantage of a model in order to improve the system's performance. This idea is paired her desire to understand mathematical solutions of the problems of well-posedness and regularity, stabilization and stability, and optimal control for finite or infinite horizon problems and existence and uniqueness of associated Riccati equations. In Mathematical Control Theory of Coupled PDEs, Lasiecka studies this concept through waves and Hyperbolic models. This book was written in order to "help engineers and professionals involved in materials science and aerospace engineering to solve fundamental theoretical control problems. Applied mathematicians and theoretical engineers with an interest in the mathematical Quantitative analysis will find this text useful." [7]

Awards and honors[4]

Publications (books)[4]

  1. Differential and Algebraic Riccati Equations with Applications to Boundary/Point Control Problems: Continuous Theory and Approximation Theory (with R. Triggiani), Springer Verlag, Lecture Notes 164, 1991, 160p.
  2. Research monograph, Deterministic Control Theory for Infinite Dimensional Systems, vols. I and II (with R. Triggiani) Encyclopedia of Mathematics, Cambridge University Press, 1999.
  3. Research monograph, Stabilization and Controllability of Nonlinear Control Systems Governed by Partial Differential Equations (with R. Triggiani) in preparation under a contract from Kluwer Academic Publishers.
  4. NSF-CMBS Lecture Notes: Mathematical Control Theory of Coupled PDE's, SIAM, 2002.
  5. Functional Analytic Methods for Evolution Equations (co-authored with G. Da Prato, A. Lunardi, L. Weis, R. Schnaubelt), Springer Verlag Lecture Notes in Mathematics, 2004.
  6. Tangential Boundary Stabilization of Navier-Stokes Equations (with V. Barbu and R. Triggiani), Memoirs of AMS, vol. 181, 2005.
  7. Long-Time Behavior of Second-Order Equations with Nonlinear Damping (with I. Chueshov),  Memoirs of AMS, Vol. 195, 2008.
  8. Von Karman Evolutions (with I. Chueshov), Monograph Series, Springer Verlag, 2010.
  9. SISSA Lecture Notes: Well-Posedness and Long-Time Behavior of Second-Order Evolutions with Critical Exponents, AMS Publishing, to appear.

Irena has written and edited numerous research journals and articles in addition to the above books.

References

  1. ↑ Faculty profile, Univ. of Memphis, retrieved 2014-12-17.
  2. ↑ Irena Lasiecka at the Mathematics Genealogy Project
  3. ↑ List of Fellows of the American Mathematical Society, retrieved 2014-12-17.
  4. 1 2 3 4 "University of Virginia". University of Virginia. Retrieved 2016-12-04.
  5. ↑ Stewart, James (2012). Brief Applied Calculus. Belmont, CA: Richard Stratton. pp. 256–257.
  6. ↑ Lasiecka, Irena. Contemporary Mathematics: Optimization Methods in Partial Differential Equations.
  7. 1 2 Lasiecka, Irena (2007). Mathematical Control Theory of Coupled PDEs. Philadelphia, PA: Society for Industrial and Applied Mathematics. pp. xi–7. ISBN 0-89871-486-9.
  8. ↑ Control of Mobile Robots (2014-03-01), 1.2 What 's Control Theory, Anyway | Control of Mobile Robots | Free online Courses 2014, retrieved 2016-12-04
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