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Optimal Control, 6 credits
Optimal styrning, 6 hp
TSRT08
Main field of study
Electrical EngineeringCourse level
Second cycleCourse type
Programme courseExaminer
Anders HanssonDirector of studies or equivalent
Johan LöfbergEducation components
Preliminary scheduled hours: 56 hRecommended self-study hours: 104 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Electrical EngineeringCourse level
Second cycleAdvancement level
A1XCourse offered for
- Industrial Engineering and Management - International, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Mathematics, Master's programme
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Automatic ControlIntended learning outcomes
Optimal control consists of theory and methods for controlling dynamical systems so that a mathematical criterion is minimized. The course aims at giving basic theory and engineering oriented computational methods in the area. After taking the course the participants are expected to be able to:
- Analyze and synthesize optimal open loop control signals using the Maximum principle.
- Analyze and synthesize optimal feedback laws using the Hamilton-Jacobi-Bellman equation.
- Use numerical software to solve optimal control problems.
- Describe the connections between optimal control and other optimization approaches.
Course content
Formulation of the optimal control problem. The Maximum Principle. Optimal feedback and the Hamilton-Jacobi-Bellman equation. Numerical methods for solving optimal control problems. Relations to MPC and convex optimization.
Teaching and working methods
The course consists of lectures, problem solving sessions and hand-in assignments.
Examination
| UPG1 | Hand-in assignments | 2 credits | U, G |
| TEN1 | Written examination | 4 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Institutionen för systemteknikDirector of Studies or equivalent
Johan LöfbergExaminer
Anders HanssonCourse website and other links
http://www.control.isy.liu.se/student/tsrt08/Education components
Preliminary scheduled hours: 56 hRecommended self-study hours: 104 h
Course literature
Additional literature
Compendia
- Ulf Jönsson, Claes Trygger, Petter Ögren, Optimal Control
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| UPG1 | Hand-in assignments | 2 credits | U, G |
| TEN1 | Written examination | 4 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Additional literature
Compendia
Ulf Jönsson, Claes Trygger, Petter Ögren, Optimal Control
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
|
|
X
|
TEN1
UPG1
|
||
| 1.2 Fundamental engineering knowledge (G1X level) |
|
X
|
X
|
TEN1
UPG1
|
||
| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
X
|
X
|
|
TEN1
UPG1
|
||
| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
|
|
|
|||
| 1.5 Insight into current research and development work |
|
|
|
|||
| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
|
X
|
|
UPG1
|
||
| 2.2 Experimentation, investigation, and knowledge discovery |
|
X
|
|
UPG1
|
||
| 2.3 System thinking |
|
X
|
X
|
TEN1
UPG1
|
||
| 2.4 Attitudes, thought, and learning |
|
|
X
|
TEN1
UPG1
|
||
| 2.5 Ethics, equity, and other responsibilities |
|
|
|
|||
| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
|
|
|
|||
| 3.2 Communications |
|
|
X
|
UPG1
|
||
| 3.3 Communication in foreign languages |
|
|
|
|||
| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
X
|
|
|
|||
| 4.2 Enterprise and business context |
|
|
|
|||
| 4.3 Conceiving, system engineering and management |
X
|
X
|
|
TEN1
UPG1
|
||
| 4.4 Designing |
|
|
|
|||
| 4.5 Implementing |
X
|
X
|
|
UPG1
|
||
| 4.6 Operating |
|
|
|
|||
| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
|
|
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| 5.2 Economic conditions for knowledge development |
|
|
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| 5.3 Identification of needs, structuring and planning of research or development projects |
|
|
|
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| 5.4 Execution of research or development projects |
|
|
|
|||
| 5.5 Presentation and evaluation of research or development projects |
|
|
|
|||
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