Optimal Control
Optimal styrteori

FRT105F, 7.5 högskolepoäng

Gäller från och med: Autumn 2023
Beslutad av: FN1/Anders Gustafsson
Datum för fastställande: 2014-03-12

Allmänna uppgifter

Avdelning: Automatic Control
Kurstyp: Ren forskarutbildningskurs
Undervisningsspråk: English

Syfte

Optimal control is the problem of determining the control function for a dynamical system to minimize a cost related to the system trajectory. The subject has its roots in the calculus of variations but it evolved to an independent branch of applied mathematics and engineering in the 1950s. The overall goal of the course is to provide an understanding of the main results in calculus of variations and optimal control, and how these results can be used in various applications such as in robotics, finance, economics, and biology

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• - understand Bellman principle of optimality,
• - understand the essential ideas of the Pontryagin Maximum Principle,
• - know the advantages and disadvantages of both dynamic programming and Pontryagin Maximum Principle.

Färdighet och förmåga

För godkänd kurs skall doktoranden

• - learn how to derive the Bellman/HJB equation for optimal control problems using dynamic programming,
• - learn how to solve low dimensional optimal control problems using Pontryagin's Maximum Principle,
• - be able to implement numerical methods to solve optimal control problems.

Kursinnehåll

Dynamic programming. Pontryagin's maximum principle. Linear quadratic regulator. Numerical methods for optimal control problems.

Kurslitteratur

• Liberzon, D.: Calculus of variations and optimal control theory: a concise introduction. Princeton university press, 2011.
• Bertsekas, D.: Dynamic programming and optimal control: Volume I. Athena scientific, 2012.

Lecture notes written by lectures

Kursens undervisningsformer

Undervisningsform: Föreläsningar

Kursens examination

Examinationsformer: Skriftlig tentamen, skriftlig rapport
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förkunskapskrav: Linear control systems

Övrig information

The course will be given only when there are at least 6 attendants.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvariga:

• Pontus Giselsson <pontus.giselsson@control.lth.se>
• Dongjun Wu <dongjun.wu@control.lth.se>