Vrije Universiteit - Divisie Wiskunde en Informatica
/Free University - Division Mathematics and Informatics
Course Mathematical Control and System Theory -
Stochastic Control in Continuous Time
/Kaput College Systeem- en Regeltheorie - Stochastische Regeltheorie in
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Course guide
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Contents of this page
Dates and times: 6 September through 6 December 2001, 13:45 - 15:30 hours
Room R2.49, Building WN, Vrije Universiteit
Jan H. van Schuppen (Lecturer)
Note, the lecture of Thursday 6 September will be postponed.
The first lecture of the class will be held on Thursday 13 September.
Jan H. van Schuppen (Lecturer)
Office WN-R3.50. JHvS is present at the Vrije Universiteit
only on Thursdays.
He can be reached at CWI on the other weekdays.
Divisie Wiskunde en Informatica, Faculteit Exacte Wetenschappen,
Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam/
Department of Mathematics and Informatics, Faculty of Exact Sciences,
Free University, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Tel. +31 20 444 7683 (VU, Thursdays)
Tel. +31 20 592 4085 (CWI, Mo, Tu, Wd, Fr)
Fax +31 20 444 7653
Email schuppen@cs.vu.nl and J.H.van.Schuppen@cwi.nl
The topic of the course changes from year to year. The topic of the
course presented in the year 2001 is
`Stochastic Control in Continuous Time'.
The aim of the course is to provide an introduction to the
basic concepts and results of control and system theory.
Control and signal processing problems arise in engineering,
economics, and biology. Solution of such problems requires mathematical
models in the form of dynamic systems.
In distinction with other areas of mathematics,
a dynamic system describes the relation between an input and
an output signal in terms of the state.
Stochastic differential equations and optimal stochastic control
form the focus of the course in the Fall of 2001.
The course is intended for
undergraduate mathematics students in their fourth or fifth year.
Measure and integration theory (WD233).
Knowledged of the course Mathematical System Theory (WD031)
or equivalent is useful but not required.
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Lecture 1. Probability theory.
(13 September 2001).
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Lecture 2. Stochastic processes.
(20 September 2001).
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Lecture 3. Stochastic processes - Filtrations.
(27 September 2001).
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Lecture 4. Martingale theory - Definitions and convergence theorems.
(4 October 2001).
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Lecture 5. Martingale theory - Decomposition and local martingales.
(11 October 2001, 3 class hours).
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Lecture 6. Stochastic integrals and the stochastic differentiation rule.
(18 October, 3 class hours).
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Lecture 7. Stochastic differential equations.
(1 November).
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Lecture 8. Stochastic systems - Modeling of phenomena.
(8 November 2001).
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Lecture 9. Stochastic systems - Definitions and properties.
(15 November 2001).
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Lecture 10. Stochastic control - Problem formulation.
(22 November 2001).
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Lecture 11. Stochastic control with complete observations -
Dynamic programming.
(29 November 2001).
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Lecture 12. Stochastic control with partial observations.
(6 December 2001).
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Oral exam
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Homeworksets with exercises.
Weekly homeworksets will be handed out in class every week.
Solutions to homeworksets are due at the lecturer one week after
they have been handed out but contact the lecturer
in case you cannot meet this due date.
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The course grade is based for 50% on the oral exam
and for the other 50% on the solutions to homeworksets.
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Course guide. This page at
http://www.cwi.nl/~schuppen/courses/vumath/control2001/control2001.html
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Weekly notes with information on the topics covered,
and advised and optional reading suggestions,
are provided on the web, see the links below.
Last update 27 October 2001.
This page is maintained by
Jan H. van Schuppen.