SF2852 Optimal Control Theory 7.5 credits

• Educational level

  Second cycle

• Academic level (A-D)

  D

• Subject area

  Mathematics
  

• Grade scale

  A, B, C, D, E, FX, F

• Link to homepage

• Course page on KTH Social

Learning outcomes

The overall goal of the course is to provide an understanding of the main results in optimal control and how they are used in various applications in engineering, economics, logistics, and biology.

Measurable goals:

To pass the course, the student should be able to do the following:

• Describe how the dynamic programming principle works (DynP) and apply it to discrete optimal control problems over finite and infinite time horizons,
• Use continuous time dynamic programming and the associated Hamilton-Jacobi-Bellman equation to solve linear quadratic control problems,
• Use the Pontryagin Minimum Principle (PMP) to solve optimal control problems with control and state constraints,
• Use Model Predictive Control (MPC) to solve optimal control problems with control and state constraints. You should also be able understand the difference between the explicit and implicit MPC control and explain their respective advantages.
• Formulate optimal control problems on standard form from specifications on dynamics, constraints and control objective. In addition be able to explain how various control objectives affect the optimal performance.
• Explain the principles behind the most standard algorithms for numerical solution of optimal control problems and use Matlab to solve fairly simple but realistic problems.

To receive the highest grade, the student should in addition be able to do the following:

• Integrate the tools learnt during the course and apply them to more complex problems.
• Explain how PMP and DynP relates to each other and know their respective advantages and disadvantages. In particular, be able to describe the difference between feedback control versus open loop control and also be able to compare PMP and DynP with respect to computational complexity.
• Combine the mathematical methods used in optimal control to derive the solution to variations of the problems studied in the course.

Course main content

Dynamic programming in continuous and discrete time. Hamilton-Jacobi-Bellman equation. Theory of ordinary differential equations. The Pontryagin maximum principle. Linear quadratic optimization. Model predictive control Infinite horizon optimal control problems. Sufficient conditions for optimality. Numerical methods for optimal control problems.

Eligibility

In general:

150 university credits (hp) including 28 hp in Mathematics,  6 hp in Mathematical Statistics and 6 hp in Optimization. Documented proficiency in English corresponding to English B.

More precisely for KTH students:

Passed courses in calculus, linear algebra, differential equations, mathematical statistics, numerical analysis, optimization.

Prerequisites

The prerequisites is a Swedish or foreign degree equivalent to Bachelor of Science of 180 ECTS credits, with at least 45 ECTS credits in mathematics. The students should have documented knowledge corresponding to basic university courses in analysis, linear algebra, numerical analysis, differential equations and transforms, mathematical statistics, and optimization.

Literature

Lecture notes from the department.

Examination

• HEM1 - Exercises, , grade scale: A, B, C, D, E, FX, F
• TEN1 - Examination, 7.5 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

A written examination (TEN1; 7,5 hp).
Optional homeworks give bonus credit on the exam.

Offered by

SCI/Mathematics

Examiner

Johan Karlsson <johan79@kth.se>

Version

Course plan valid from: Spring 11.
Examination information valid from: Autumn 07.