Official Information  

Course Number:  Math 8200.001 
CRN:  28667 
Course Title:  Topics in Applied Mathematics: Control Theory and Practice 
Times:  TR 9:3010:50 
Places:  Wachman 527 
Instructor:  Benjamin Seibold 
Instructor Email:  seibold(at)temple.edu 
Instructor Office:  518 Wachman Hall 
Instructor Office Hours:  TR 11:0012:00 
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, PDEconstrained 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: openloop 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
Read:
Hautus lemma,
Kalman decomposition

09/11/2018 Lec 5  Asymptotic controllability

09/13/2018 Lec 6  Nonlinear control problems

09/18/2018 Lec 7  Accessibility

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, controllabilityobservabilityduality

10/16/2018 Lec 14  Nonlinear systems and zeroinput 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  Linearquadratic 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  Bangbang principle
Read:
Bangbang control

11/27/2018 Lec 25  Linear timeoptimal control

11/29/2018 Lec 26  Pontryagin maximum principle

12/04/2018 Lec 27  Dynamic programming, HamiltonJacobiBellman equation

12/06/2018 Lec 28  PDEconstrained optimization

12/13/2018  Final Examination 