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Syllabus for

Academic year
SSY235 - Advanced topics in control
Syllabus adopted 2015-02-17 by Head of Programme (or corresponding)
Owner: MPSYS
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Automation and Mechatronics Engineering, Electrical Engineering, Engineering Physics

Teaching language: English
Open for exchange students
Block schedule: A

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0109 Written and oral assignments 3,0 c Grading: UG   3,0 c    
0209 Examination 4,5 c Grading: TH   4,5 c   16 Jan 2016 pm M,  05 Apr 2016 pm M,  16 Aug 2016 pm M

In programs



Professor  Claes Breitholtz


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

  1. A basic course in automatic control including state space models.

  2. The MPSYS-course "Linear control system design" is required.

  3. The MPSYS-course "Nonlinear and adaptive control" is recommended.


The purpose is to introduce the students to concepts of control, frequently encountered in the technical and scientific literature on control, hence decreasing "the barrier" for the student to penetrate more demanding material. The topic of classical optimal control is chosen to fulfil this purpose for the current academic year.

Learning outcomes (after completion of the course the student should be able to)

* Have knowledge on calculus of variations and its application to optimal control problems. Be able to solve such problems analytically or by use of computers.
* Have knowledge of linear quadratic optimal control problems at the level of understanding proofs of some relevant theorems, but also be able to solve such problems hands on. The continuous time case is emphasized in this course.
* Understanding the fundamental concepts of the Pontryagin minimum principle, Dynamic programming and its continuous time extension, the Hamilton-Jacoby-Bellman equation.
* Have knowledge of how to apply the Pontryagin principle to constrained optimal control problems, in particular minimum time problems.
* Have knowledge on the stochastic version of the Hamilton-Jacoby-Bellman equation at an introductory level.


* Some historical notes on calculus of variations and optimal control. The Euler-Lagrange equation, interpretation of its boundary conditions and importance of the second variation.
* Linear quadratic optimal control systems. The finite-time linear quadratic regulator. The Riccati differential equation and its solution methods and properties. The linear quadratic tracking problem. Linear quadratic optimal control for time-varying systems.
* Infinite-time linear quadratic regulator. The Riccati algebraic equation. Frequency domain properties, in particular robustness properties.
* The Pontyagin minimum principle. The principle of optimality and dynamic programming. The Hamilton-Jacoby-Bellman partial differential equation.                                                   * Optimal control problems with constraints. Minimum time problems, minimum energy and minimum fuel problems.                                                                                         *Wiener processes, white noise and stochastic differential equations. The stochastic Hamilton-Jacoby-Bellman partial differential equation applied to an inventory problem.


The course comprises lectures, integrated exercises and a number of assignments with  tutoring.


The book "Optimal Control Systems" by Desineni Subbaram Naidu, CRC Press
2003. Some complementary material on stochastic control and assignment


Handed in and passed assignments is a necessary requirement to pass the course. To obtain the grades 4 and 5, satisfactory results in a written examination is in addition required.

Page manager Published: Mon 28 Nov 2016.