M7860 Theory of regulation and optimalization

Faculty of Science
Autumn 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:
M7860/01: Wed 19:00–19:50 UP1
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
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.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009.
  • Enrolment Statistics (Autumn 2008, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2008/M7860