# Introduction to mathematical physics, fall 2013

# Introduction to Optimal Control

### Lecturer

Paolo Muratore-Ginanneschi

Kay Schwieger

### Description

The aim of the course is to provide an overview of methods and applications of deterministic

and stochastic control theory to mechanics and statistical physics. The course will start by

recalling basic concepts from variational calculus (Euler–Lagrange and Hamilton equations).

It will then proceed with an elementary introduction to Pontryagin theory for optimal control

of systems governed by differential equations. After an heuristic introduction to stochastic

systems, the aim of the second part of the course is to expound the basic ideas of optimal

control of system governed by stochastic differential equations.

### Scope

10 sp.

### Type

Advanced studies

### Prerequisites

The course is intended for advanced undergraduate students of mathematics, physics, chemistry

and mathematical economics. Prior courses in advanced calculus and linear algebra are

required (Diff.Int. 1-2 and Lineaarialgebra 1, or Mapu 1-2). Background material will be on

request discussed during the course

### Lectures

Weeks 36-42 and 44-50, Tuesday 14-16 in room C124, and Friday 14-16 in room C123.

First lecture Friday September the 6th in C123

### Exams

### Bibliography

The course will mainly follow

Lawrence Craig Evans, "

*An Introduction to Mathematical Optimal Control Theory*" Berkeley lecture notes

Other useful references may be

- Ramon van Handel, "
*Stochastic Calculus and Stochastic Control*" Caltech Lecture Notes - Leonard Christopher Gordon Rogers, "
*Duality in constrained optimal investment and consumption problems: a synthesis*" Paris-Princeton Lectures on Mathematical Finance - Wendell Helms Fleming and, Mete Halil Soner, "
*Controlled Markov processes and viscosity solutions*" Springer 2006. - Anastasios G. Malliaris and William A. Brock, "
*Stochastic methods in economics and finance*" Elsevier Science 1999 - Fwu-Ranq Chang, "
*Stochastic optimization in continuous time*" Cambridge University Press 2004

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