Course syllabus

Course-PM

SSY235 Advanced topics in control lp2 HT19 (7.5 hp)

Course is offered by the department of Electrical Engineering

Contact details

Examiner and lecturer: 
Claes Breitholtz (claesbr@chalmers.se), room 5345 (available by appointment)

Teaching assistants:
Rémi Lacombe (lacombe@chalmers.se), room 5340 (available by appointment)
Elena Malz (elenama@chalmers.se), room 5343 (available by appointment)

Department exam office:
Madeleine Persson (studadm.e2@chalmers.se), room 3342

Course purpose

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. 

Schedule

Please find the course schema in Time Edit.

Alternatively, find the course program as pdf under "Files".

Course literature

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

Course design

Lectures:

The course consists of lectures twice a week and tutoring sessions once a week.

Assignments:

The assignments will be performed in a group of maximum two students. You can form the groups individually on Canvas by assigning to a free group. Please stay in the same groups for all assignments. The deadline of each assignment is given when the assignments are published. This will be announced on Canvas. For the hand-in, please provide a pdf ( computer- or hand-written) and submit it to the assignment page on Canvas. Each assignment will be graded  as 'Completed' or 'Incomplete'. In case the assignment is marked as 'Incomplete', a revision has to be submitted before the oral examination. The assignments will be accomplished after a passed oral examination.

Oral examination:

All assignments will be discussed during oral examinations, held for each student group individually. The oral examinations will go through the assignments and check for general understanding of the topic. In order to limit the occations for the examinations multiple assignments will be combined. Thus, there will be around 3 examinations in total.  The dates for the oral examinations are not fixed yet, but they will be announced on Canvas right in time. For each examination, there will be a spread sheet with different dates and time slots which can be picked by you as a group. The first spread sheet with possible slots for the first examination will be online in week 46.

The course is covered by the text book, with exception of the stochastic control part. 

Learning objectives

• 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.

Course content

• 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.

Examination form

A necessary and sufficient condition for a master student to pass the course is satisfactory completion of all assignments. An assignment is approved when the report is correct and the tutor has put oral questions to both students. A written examination of 20 points is given, Saturday, January, 18, 2020, 14.00-18.00. Result required for each grade:

Grade 3 : passed assignments - exam is not mandatory (for master students)

Grade 4 : 9 points in the exam

Grade 5 : 15 points in the exam

Note for PhD-students: The criterion for passed in case of PhD students is firstly the same as for master students and secondly at least 12 points at the written examination.