SF2842 Geometric Control Theory 7.5 credits

Geometrisk styrteori

  • Education cycle

    Second cycle
  • Main field of study

    Mathematics
  • Grading scale

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

Course offerings

Spring 19 SAP for Study Abroad Programme (SAP)

  • Periods

    Spring 19 P3 (7.5 credits)

  • Application code

    20059

  • Start date

    15/01/2019

  • End date

    15/03/2019

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places

    No limitation

  • Course responsible

    Xiaoming Hu <hu@kth.se>

  • Target group

    Study Abroad Programme

  • Application

    Apply for this course at antagning.se through this application link.
    Please note that you need to log in at antagning.se to finalize your application.

Intended learning outcomes

This is an advanced course in mathematical systems theory. With the geometric control theory in focus, this course deepens and broadens knowledge and introduces new concepts in the subject. The course aims at that the student can use the geometric approach to treat basic control design and analysis problems for both linear systems and some nonlinear systems. The knowledge and skill acquired in this course also help enhance the student's ability for abstracting engineering problems.

The overall goal of the course is that the student understands and appreciates the theory and various tools in the geometric approach to systems and control; in particular the student should be able to use the underlying methodologies in practical applications.

Measurable goals

After having finished the course the student should be able to do the following:

  • Reinterpret basic control properties such as Controllability and Observability for linear systems as the property of certain invariant subspace.
  • Understand the geometric interpretation of transmission zeros and zero dynamics.
  • Compute invariant subspaces and various controlled invariant subspaces.
  • Apply different algorithms to solve control problems such as DDP, non-interacting control, tracking and output regulation.
  • Explain how the steady state output response is shaped by the input signal.
  • Solve some basic control problems for nonlinear systems that do not have a controllable linearized system.

For the highest grade the student should be in addition able to

  • Explain how the above results and methods relate and build on each other.
  • Explain the mathematical foundation and control implication of the results and algorithms studied in the course.
  • Solve simple but realistic control problems that require the synthesis of different design algorithms.

Course main content

Introduction and motivation, Invariance and controlled invariance, Zeros, Zero dynamics and system inversion, Tracking and non-interacting control, Disturbance decoupling, Internal model principle, Spectral factorization, Nonlinear systems, Geometric control of robotic systems.

Eligibility

In general:

150 university credits (hp) including 28 hp in Mathematics, 6 hp in Mathematical Statistics and 6 hp in Control Theory. 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, control theory. A passed course in mathematical systems theory (SF2832) is an advantage.

Literature

Geometric Control Theory, lecture notes by Hu and Lindquist.

Examination

  • TENA - Examination, 7.5, grading scale: A, B, C, D, E, FX, F

Requirements for final grade

Written examination (TENA; 7,5 hp).

Offered by

SCI/Mathematics

Contact

Xiaoming Hu (hu@kth.se)

Examiner

Xiaoming Hu <hu@kth.se>

Supplementary information

Not given 10/11.

Version

Course syllabus valid from: Spring 2016.
Examination information valid from: Autumn 2015.