Course 8200 - Topics in Applied Mathematics: Control Theory and Practice - Fall 2018

Official Information
Course Number:Math 8200.001
Course Title:Topics in Applied Mathematics: Control Theory and Practice
Times:TR 9:30-10:50
Places:Wachman 527
Instructor: Benjamin Seibold
Instructor Email: seibold(at) 
Instructor Office:518 Wachman Hall
Instructor Office Hours:TR 11:00-12:00
Course Textbooks: There is no single textbook for this course. The materials come from a variety of books and online materials. Recommended reading:
  • Eduardo Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, Second Edition, Springer, 1998
  • Eva Zerz, Introduction to Systems and Control Theory, Lecture Notes, Aachen
  • Karl Johan Astrom, Richard M. Murray, Feedback Systems, Princeton University Press, 2012
  • Lawrence C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, American Mathematical Society, 1998
  • Lawrence C. Evans, An Introduction to Mathematical Optimal Control Theory, Lecture Notes, 1983
  • Neculai Andrei, Modern Control Theory - A historical perspective, 2005
Official:Course Syllabus
Topics Covered: This course provides an overview over numerous aspects of Control Theory and related topics, including (A) fundamental theory: systems theory, linear control theory, controllability, observability, reachability, pole shifting, open vs. closed loop control, transfer functions; (B) a selection (depending on students' interest) of advanced topics, such as: optimal control, PDE-constrained optimization, adjoint calculus, differential games; and (C) practice: applications of controllers, parameter choices in PID controllers, computational methods, robotics.
Course Goals: Provide both a rigorous mathematics background of control theory, as well as a good feel and intuition for the underlying ideas and mechanisms. Expose students to practical challenges in computation and application in actual physical systems.
Attendance Policy: Students are expected to attend every class. If a student cannot attend a class for some justifiable reason, he or she is expected to contact the instructor before class.
Course Grading: Homework/projects: 50%; exams: 50%.
Final Exam Date:12/13/2018.
Course Schedule
08/28/2018   Lec 1
Introduction: open-loop vs. feedback, pole shifting
08/30/2018   Lec 2
Dynamic feedback, PID controller
   Read: PID controller
09/04/2018   Lec 3
Controllability: controllability matrices, minimal energy
09/06/2018   Lec 4
Hautus test, fundamental forms, Kalman controllability decomposition
09/11/2018   Lec 5
Asymptotic controllability
09/13/2018   Lec 6
Nonlinear control problems
09/18/2018   Lec 7
09/20/2018   Lec 8
Feedback control: pole placement
   Read: Full state feedback
09/25/2018   Lec 9
Stabilization, feedback equivalence
09/26/2018   Lec 10
Brunovsky form, stabilization of nonlinear control problems
10/02/2018   Lec 11
Control as interconnection
10/04/2018   Lec 12
Observability: matrices, fundamental forms
   Read: Observability
10/09/2018   Lec 13
Kalman observability decomposition, asymptotic observability, controllability-observability-duality
10/16/2018   Lec 14
Nonlinear systems and zero-input observability
10/17/2018   Lec 15
Observers: pole placement, compensators
   Read: State observer
10/23/2018   Lec 16
Transfer matrices: realization theory
10/24/2018   Lec 17
Poles and zeros
   Read: Systems theory
10/25/2018   Lec 18
Frequency domain modeling: Laplace transform
10/30/2018   Lec 19
Transfer functions, system response
11/01/2018   Lec 20
Engineering perspective: block diagrams, Lyapunov stability, delay
   Read: Lyapunov stability
11/06/2018   Lec 21
Linear-quadratic regulator, Kalman filter, Bode plot
11/07/2018   Lec 22
Optimal control: framework, examples
   Read: Optimal control
11/08/2018   Lec 23
Controllability with constraints
   Read: Constraint
11/13/2018   Lec 24
Bang-bang principle
   Read: Bang-bang control
11/27/2018   Lec 25
Linear time-optimal control
11/29/2018   Lec 26
Pontryagin maximum principle
12/04/2018   Lec 27
Dynamic programming, Hamilton-Jacobi-Bellman equation
12/06/2018   Lec 28
PDE-constrained optimization
12/13/2018 Final Examination