MATH 3902 Spring Semester 2017

Advanced Scientific Computing - Optimal Control of Partial Differential Equations
MWF 12:00-12:50PM, Thackeray Hall 624

Office Hours

MWF 3:00 - 4:00, and by appointment
Office: Thackeray 606
Phone: (412) 624 5681

This course is an introduction to modern for optimal control and optimization. Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences and other disciplines. We shall focus on optimal control problems where the state equation is an elliptic of parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, numerical algorithms and implementation techniques. The expositions begins with control problems with linear equations, quadratic cost functions and control constraints. The course is self-contained, basic facts on weak solutions of elliptic and parabolic equations, principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties.

Written homework and several computational projects will be assigned. The suggested programming language for computer assignments is Matlab, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows in the university computing labs. The full set of manuals is on the web in html and also in Adobe PDF format. The "Getting Started" manual is a good place to begin and is available both in html format and in Adobe PDF format. The full reference manual as well as manuals for each of the many toolboxes are all available.

Course materials

  • Optimal Control Theory of Partial Differential Equations. Theory, Methods and Applications, by Fredi Tröltzsch.

  • Additional references
  • Optimization with PDE constraints, by Michael Hinze, Rene Pinnau, Michael Ulbrich and Stefan Ulbrich.
  • An Introduction to Optimal Control Problems in Life Sciences and Economics From Mathematical Models to Numerical Simulation with MATLAB, by Sebastian Aniţa, Viorel Arnăutu, Vincenzo Capasso.

  • Disability Resource Services

    If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

    Academic Integrity

    Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a zero score for the quiz, exam or paper in question. Additional sanctions may be imposed, depending on the severity of the infraction. On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.

    Statement on Classroom Recording

    To address the issue of students recording a lecture or class session, the University's Senate Educational Policy Committee issued the recommended statement on May 4, 2010. "To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student's own private use."