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ECSE 6440/MANE 6964 Optimal Control (Spring 2012)

Text: Daniel Liberzon, Calculus of Variations & Optimal Control Theory, Princeton University Press, 2012


  • A. Bryson and Y.C. Ho, Applied Optimal Control , Hemisphere Pub, 1981.
  • F.L. Lewis and V.L. Syrmos, Optimal Control, 2nd Ed.,Wiley Interscience, 1995.
  • S.P. Sethi and G. L. Thompson, Optimal Control Theory, Kluwer Academic, 2000.
  • Donal Kirk, Optimal control theory: an introduction, Prentice-Hall, 1970.
  • B.D.O. Anderson and J.B. Moore, Linear Optimal Control, Prentice-Hall, 1971.
  • B.D.O. Anderson and J.B. Moore, Optimal Filtering, Prentice-Hall, 1979.
  • G.E. Dullerud and F.G. Paganini, A course in robust control theory, Springer, 2000.
  • J.C. Doyle, B.A. Francis, A.R.Tannenbaum, Feedback Control Theory, 1992.

Prerequisites: ECSE 6400 (Systems Analysis Techniques) or equivalent.

Course website: http://www.cats.rpi.edu/~wenj/ECSE644S12

Course Objective: This course covers the basic concepts, techniques, and tools related to optimal control for dynamical systems.  Major topics include calculus of variation, minimum principle, dynamic programming. Both discrete time systems and continuous times are addressed.  Particular consideration is given to application to multivariable linear time invariant systems in terms of H2 and H optimal control.

Learning Outcomes:Students who complete this course satisfactorily will be able to: (i) formulate first order optimality condition for calculus of variation and optimal control problem, (ii) find optimal control by solving for two-point boundary value problem, (iii) find otpimal control for linear time invariant systems by solving the corresponding Riccati equations, (iv) formulate multi-player (game theoretic) optimal control problem

Grade Composition:

Final Exam

Homework:Homework will account for 20% of the course grade.  Problems will be assigned roughly in 1-2 week intervals. The problems are best done individually in a professional manner (neatness counts!).  Solutions will be posted shortly after the homework is handed in in class.  Collaboration in the solution of the homework problems is permitted but individual work must be handed in and mere copying of the solution is not allowed.  In general, no late assignments will be accepted.  However, extensions may be granted if a situation arises for which it is warranted.  In these instances the student must request the extension in writing prior to the assignment due date, stating the reason for the request and the date the assignment is to be submitted.

Project: Project will account for 25% of the course grade. Up to two persons may collaborate on a project, but both must sign a statement describing the respective contribution. The project report is due at the end of the semester.

Homework and project may require the use of MATLAB and relevant toolboxes.  

Exam: Midterm and final exams will both be take-home exames.  Absolutely no collaboration is allowed for the take-home exams.

Statement of Academic Integrity
Student-teacher relationships are built on trust. The students must trust that the instructor has made appropriate decisions about the structure, content, etc., of the courses they teach, and the instructors must trust that assignments which students turn in are their own. Acts which violate this trust undermine the education process.
The Rensselaer Handbook defines various forms of Academic Dishonesty and procedures for dealing with them. All forms are violations of the trust between the students and instructors. All students should familiarize themselves with this portion of the Rensselaer Handbook and should note that the penalties for the various forms of dishonesty can be quite harsh. Cheating will result in a zero on the associated assignment, and referral to the Dean of Students for possible additional action.
All cell phones are to be turned off during exams. Cell phone usage including texting of any kind during and exam will be considered cheating, and will result in a zero for the exam.