| Official Information | |
|---|---|
| Course Number: | Math 8200.001 |
| CRN: | 50548 |
| Course Title: | Topics in Applied Mathematics: Control Theory |
| Times: | MW 1:00-2:20 |
| Places: | Wachman 617 |
| Instructor: | Benjamin Seibold |
| Instructor Email: | seibold(at)temple.edu |
| Instructor Office: | 518 Wachman Hall |
| Instructor Office Hours: | MW 2:20-3:30 |
| Course Textbooks: |
There is no single textbook for this course. The materials come from a variety of books and online materials. Recommended reading:
|
| Official: | Course Syllabus |
| Prerequisites: | none |
| 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. |
| 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: | Semester assignments: 50%; final examination: 50%. |
| Final Exam Date: | 12/15/2023. |
| Course Schedule | |
| 08/28/2023 Lec 1 | Introduction: open-loop vs. feedback, pole shifting
|
| 08/30/2023 Lec 2 | Dynamic feedback, PID controller
Read:
PID controller
|
| 09/06/2023 Lec 3 | Controllability: controllability matrices, minimal energy
|
| 09/11/2023 Lec 4 | Hautus test, fundamental forms, Kalman controllability decomposition
Read:
Hautus lemma,
Kalman decomposition
|
| 09/13/2023 Lec 5 | Asymptotic controllability
|
| 09/18/2023 Lec 6 | Nonlinear control problems
|
| 09/20/2023 Lec 7 | Accessibility
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| 09/25/2023 Lec 8 | Feedback control: pole placement
Read:
Full state feedback
|
| 09/27/2023 Lec 9 | Stabilization, feedback equivalence
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| 10/02/2023 Lec 10 | Brunovsky form, stabilization of nonlinear control problems
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| 10/04/2023 Lec 11 | Control as interconnection
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| 10/09/2023 Lec 12 | Observability: matrices, fundamental forms
Read:
Observability
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| 10/11/2023 Lec 13 | Kalman observability decomposition, asymptotic observability, controllability-observability-duality
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| 10/16/2023 Lec 14 | Nonlinear systems and zero-input observability
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| 10/18/2023 Lec 15 | Observers: pole placement, compensators
Read:
State observer
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| 10/23/2023 Lec 16 | Transfer matrices: realization theory
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| 10/25/2023 Lec 17 | Poles and zeros
Read:
Systems theory
|
| 10/30/2023 Lec 18 | Frequency domain modeling: Laplace transform
|
| 11/01/2023 Lec 19 | Transfer functions, system response
|
| 11/06/2023 Lec 20 | Engineering perspective: block diagrams, Lyapunov stability, delay
Read:
Lyapunov stability
|
| 11/08/2023 Lec 21 | Linear-quadratic regulator, Kalman filter, Bode plot
|
| 11/13/2023 Lec 22 | Optimal control: framework, examples
Read:
Optimal control
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| 11/15/2023 Lec 23 | Controllability with constraints
Read:
Constraint
|
| 11/27/2023 Lec 24 | Bang-bang principle
Read:
Bang-bang control
|
| 11/29/2023 Lec 25 | Linear time-optimal control
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| 12/04/2023 Lec 26 | Pontryagin maximum principle
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| 12/06/2023 Lec 27 | Dynamic programming, Hamilton-Jacobi-Bellman equation
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| 12/08/2023 Lec 28 | PDE-constrained optimization
|
| 12/15/2023 | Final Examination |