CHALMERS UNIVERSITY OF TECHNOLOGY

Department of Applied Mechanics

Division of Dynamics

 

PM

Graduate Course

Optimization of Dynamic Systems

 

Quarter 1

2007/2008 Academic Year

 

 

 

Credits: 5 credit units, (ECTS 7,5)

 

Institution: Department of Applied Mechanics

Teaching Language: English

Course home page: http://www.am.chalmers.se/~berbyuk/ods.htm

 

Course aim

The Graduate Course “Optimization of Dynamic Systems” aims to meet requirements and needs of beginning and senior PhD students in algorithms, methods and knowledge of optimization of broad classes of dynamic systems: general evolutional systems, controlled mechanical systems, electro-magneto-elastic systems, smart systems for active vibration control, others.

Course outline

The course is based on the book ’Practical Methods for Optimal Control Using Nonlinear Programming’ by John T. Betts, 2001. This is quite possibly the first book on practical methods that combines nonlinear optimization, mathematical control theory, and numerical solution of ordinary differential or differential-algebraic equations to successfully solve optimal control problems. The focus of the course is on practical methods, i.e., methods that were found to actually work.

 

The lectures of the topic of the course will maintain a focused and concise presentation. Using modern computational methods based on nonlinear programming algorithms, the basic material necessary to solve an optimal control problem will be introduced. Two major parts of a successful optimal control solution technique will be considered. The first part is the optimization methods. The second part is the differential equation methods. It will be demonstrated that the methods used to solve differential equations and optimize the functions are intimately related. Many examples that illustrate the various concepts and techniques will be considered in the course. The examples which are based on student own PhD projects will also be under the studied.

Course contents

A course “Optimization of Dynamic Systems” is based on several lectures, discussion meeting-seminars, own student studies and two written assignments, which require computer implementation of numerical methods. The following topics will be covered:

·       Introduction to Nonlinear Programming

·       Large, Sparse Nonlinear Programming

·       Optimal Control Preliminaries

·       The Optimal Control Problems

·       Optimal Control Examples.

 

Audience

The material is presented at a level suitable for most engineering students interested in practical applications. The textbook and the course itself are oriented toward students interested in solving practical optimization problems for different dynamic systems. Although the first few chapters refresh the reader's knowledge of nonlinear optimization, mathematical control theory, and numerical solution of ordinary differential and/or differential-algebraic equations, course participants will need at least an introductory background on this material.

 

Course literature

The course is based on the book “Practical Methods for Optimal Control Using Nonlinear Programming” by John T. Betts, 2001, SIAM, Society for Industrial and Applied Mathematics / Hardcover / ISBN 0-89871-488-5. For those students that will be registered for the course before June 15, 2007 the Betts book will be ordered by the division of Dynamics and the students can borrow the book.

Course duration and examination

The course will start in beginning of September 2007. The examination consists of solutions to two assignments that will be given during the course and oral discussion between student and examiner.

Course responsible

Course teacher and examiner: Prof. Viktor Berbyuk.

Registration

Registration shall be made to Prof. Viktor Berbyuk, at the latest 29th of June 2007 via e-mail: viktor.berbyuk@chalmers.se