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Institutionernas kurser för doktorander

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Kursplan för

Läsår
SSY235 - Advanced topics in control
 
Kursplanen fastställd 2009-02-26 av programansvarig (eller motsvarande)
Ägare: MPSYS
7,5 Poäng
Betygskala: TH - Fem, Fyra, Tre, Underkänt
Utbildningsnivå: Avancerad nivå
Huvudområde: Automation och mekatronik, Elektroteknik, Teknisk fysik
Institution: 32 - ELEKTROTEKNIK


Undervisningsspråk: Engelska

Modul   Poängfördelning   Tentamensdatum
Lp1 Lp2 Lp3 Lp4 Sommarkurs
0109 Inlämningsuppgift 3,0 hp Betygskala: UG   3,0 hp    
0209 Tentamen 4,5 hp Betygskala: TH   4,5 hp   15 Dec 2010 em M,  29 Apr 2011 em V,  18 Aug 2011 em V

I program

MPSYS SYSTEMS, CONTROL AND MECHATRONICS, MSC PROGR, Årskurs 2 

Examinator:

Professor  Claes Breitholtz


Kursutvärdering:

http://document.chalmers.se/doc/630356719


Behörighet:

För kurser inom Chalmers utbildningsprogram gäller samma behörighetskrav som till de(t) program kursen ingår i.

Kursspecifika förkunskaper


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

  2. The MPSYS-course "Digital and multivariable control" is required.

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

Syfte

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 academic year 2009/2010.

Lärandemål (efter fullgjord kurs ska studenten kunna)

* Have knowledge on calculus of variations and its application to optimal control  problems. Be able to solve such problems analytically and by use of computers.
* Have knowledge of linear quadratic optimal control problems at the level of understanding proofs of some relevant theorems, but also to be able to solve such problems hands on. The continuous and discrete time cases are both considered.
* Understanding the fundamental concepts of the Pontryagin Minimum Principle, Dynamic Programming, as well as its continuous time extension, the Hamilton-Jacobi-Bellman equation.
* Have knowledge of applying the Pontryagin principle to constrained optimal control problems, in particular minimum time problems.
* Have an introductory knowledge of solving optimal control problems in the presence of stochastic disturbances.

Innehåll

* 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. Finite-time linear quadratic regulator. The Riccati differential equation, solution methods and solution properties. Linear quadratic tracking problems. Discrete time linear quadratic regulators.
* Infinite-time linear quadratic regulator. The Riccati algebraic equation, solution methods. Frequency domain properties of linear quadratic regulators. Gain and phase margins.
* The Pontryagin minimum principle. The principle of optimality and dynamic programming. The Hamilton-Jacobi-Bellman partial differential equation.
* Optimal control problems in case of stochastic disturbances, in the continuous time as well in the discrete time case.
* Optimal control problems with constraints. Minimum time problems and fuel problems. A stochastic inventory problem with state constraints.

Organisation

 The course comprises lectures and a number of supervised assignments.

Litteratur

 


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

Examination



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.




Sidansvarig Publicerad: må 13 jul 2020.