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1 = Introduction to mathematical physics, fall 2013 =
2
3 = Introduction to Optimal Control =
4
5 === Lecturer ===
6
7 [[Paolo Muratore-Ginanneschi>>doc:mathstatHenkilokunta.Muratore-Ginanneschi, Paolo]]
8 [[Kay Schwieger>>url:http://wiki.helsinki.fi/display/mathstatHenkilokunta/Schwieger,+Kay||shape="rect"]]
9
10 === Description ===
11
12 The aim of the course is to provide an overview of methods and applications of deterministic
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14 and stochastic control theory to mechanics and statistical physics. The course will start by
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16 recalling basic concepts from variational calculus (Euler–Lagrange and Hamilton equations).
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18 It will then proceed with an elementary introduction to Pontryagin theory for optimal control
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20 of systems governed by differential equations. After an heuristic introduction to stochastic
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22 systems, the aim of the second part of the course is to expound the basic ideas of optimal
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24 control of system governed by stochastic differential equations.
25
26 === Scope ===
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28 10 sp.
29
30 === Type ===
31
32 Advanced studies
33
34 === Prerequisites ===
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36 The course is intended for advanced undergraduate students of mathematics, physics, chemistry
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38 and mathematical economics. Prior courses in advanced calculus and linear algebra are
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40 required (Diff.Int. 1-2 and Lineaarialgebra 1, or Mapu 1-2). Background material will be on
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42 request discussed during the course
43
44 === Lectures ===
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46 Weeks 36-42 and 44-50, Tuesday 14-16 in room C124, and Friday 14-16 in room C123.
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48 First lecture Friday September the 6th in C123
49
50 === Exams ===
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52
53
54 === Bibliography ===
55
56 The course will mainly follow
57
58 * (((
59 Lawrence Craig Evans, "//An Introduction to Mathematical Optimal Control Theory//" [[Berkeley lecture notes>>url:https://wiki.helsinki.fi/http: /math.berkeley.edu/~~evans/control.course.pdf||shape="rect"]]
60 )))
61
62 Other useful references may be
63
64 * Ramon van Handel, "//Stochastic Calculus and Stochastic Control//" [[Caltech Lecture Notes>>url:http://www. princeton.edu/~~rvan/acm217/ACM217.pdf||shape="rect"]]
65 * Leonard Christopher Gordon Rogers, "//Duality in constrained optimal investment and consumption problems: a synthesis//" [[Paris-Princeton Lectures on Mathematical Finance>>url:http://www.statslab.cam. ac.uk/~~chris/papers/CIRANO.pdf||shape="rect"]]
66 * Wendell Helms Fleming and, Mete Halil Soner, "//Controlled Markov processes and viscosity solutions//" Springer 2006.
67 * Anastasios G. Malliaris and William A. Brock, "//Stochastic methods in economics and finance//" Elsevier Science 1999
68 * Fwu-Ranq Chang, "//Stochastic optimization in continuous time//" Cambridge University Press 2004
69
70 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57357||shape="rect"]] ===
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72
73 Did you forget to register? [[ What to do?>>doc:mathstatOpiskelu.Kysymys4]]
74
75 === Laskuharjoitukset ===
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