PřF:M7860 Theory of regul. and optim. - Course Information
M7860 Theory of regulation and optimalization
Faculty of ScienceAutumn 2008
- Extent and Intensity
- 2/1/0. 3 credit(s) (fasci plus compl plus > 4). Type of Completion: k (colloquium).
- Teacher(s)
- doc. RNDr. Erich Barvínek, CSc. (lecturer)
- Guaranteed by
- prof. RNDr. Roman Šimon Hilscher, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Wed 17:00–18:50 UP1
- Timetable of Seminar Groups:
- Prerequisites
- Differential and integral calculus of one and several variables, linear functional analysis. A knowledge of the calculus of variations is an advantage.
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Finance Mathematics (programme PřF, N-AM)
- Mathematics - Economics (programme PřF, M-AM)
- Mathematics (programme PřF, M-MA)
- Mathematics (programme PřF, N-MA)
- Course objectives
- The aim of this course is to provide theoretical and practical tools needed for solving problems in the optimal control theory. The main topic is the (weak) Pontryagin principle. The emphasis will be on the comparison of the classical calculus of variations with the theory of optimal control and on managing practical applied problems.
- Syllabus
- 1. Tools from nonlinear functional analysis 2. Methods of calculus of variations. 3. Lagrangian problems. 4. Linear-quadratic problems. 5. Problems of optimal control. 6. Pontryagin principle. 7. Classification of harmonic oscillators. 8. Optimal production model. 9. Newton's aerodynamic problem. 10. Optimal interpolation and Sobolev spaces.
- Literature
- BRESSAN, Alberto and Benedetto PICCOLI. Introduction to the mathematical theory of control. Springfield, MO, USA: American Institute of Mathematical Sciences (AIMS), 2007, 312 pp. AIMS Series on Applied Mathematics, 2. ISBN 978-1-60133-002-4. info
- GREGORY, John and Cantian LIN. Constrained optimization in the calculus of variations and optimal control theory. London: Chapman and Hall, 1996, xii, 217. ISBN 0442007221. info
- LEWIS, Frank. Optimal Control. New York: John Wiley & Sons, 1986, 362 pp. A Wiley-Interscience Publication. ISBN 0-471-81240-4. info
- BELLMAN, Richard. Introduction to the mathematical theory of control processes. Vol. II: Nonlinear processes. New York: Academic Press, 1971, 306 pp. Mathematics in Science and Engineering, Vol. 40-II. info
- BELLMAN, Richard. Introduction to the mathematical theory of control processes. Vol. 1: Linear equations and quadratic criteria. New York: Academic Press, 1967, 245 pp. Mathematics in Science and Engineering, Vol. 40. info
- Assessment methods
- Two-hour written test.
- Language of instruction
- Czech
- Further Comments
- The course is taught annually.
- Enrolment Statistics (Autumn 2008, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2008/M7860