# Course Details

Course Information Package

Course Unit TitleOPTIMAL CONTROL SYSTEMS
Course Unit CodeAEEE544
Course Unit DetailsMSc Electrical Engineering (Technical Electives) -
Number of ECTS credits allocated7
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
1. Review of Optimisation in Classical Control Theory. Perform State variable representation of a control system and appreciate the concept of the performance measure
2. Apply the optimal control law and the make decisions using the principle of optimality. Apply Recurrence relation of dynamic programming and identify the characteristics of dynamic programming solution. Derive The Hamilton-Jacobi-Bellman equation and solve the Continuous linear regulator problem.
3. Appreciate the fundamental theorem of calculus of variations and solve functionals of single function and several independent functions by using piecewise smooth extremals and constrained extremals.
4. Appreciate the use of the variational approach to optimal control problems and apply Pontryagin’s minimum principle. Apply the necessary conditions in Linear regulator problems. Solve minimum time and minimum control effort problems.
Mode of DeliveryFace-to-face
PrerequisitesNONECo-requisitesNONE
Recommended optional program componentsNONE
Course Contents

Optimisation in Classical Control: Review of optimization in classical control.

Introduction: Problem formulation; State variable representation of the system.

The performance measure: Definition; Selection, Examples.

Dynamic Programming: The optimal control law; The principle of optimality; Decision making using the principle of optimality; Routing problem; Optimal control systems; Interpolation; Recurrence relation of dynamic programming; characteristics of dynamic programming solution; The Hamilton-Jacobi-Bellman equation; Continuous linear regulator problem.

The calculus of variations: Fundamentals; The fundamental theorem of calculus of variations; Functionals of single function; Functionals involving several independent functions; Piecewise smooth extremals; Constrained extremas.

The variational approach to optimal control problems: Necessary conditions; Linear regulator problems; Pontryagin’s minimum principle; Minimum time problems; Minimum control effort problems.

Textbooks
• D.S. Naidu, “Optimal Control Systems”, CRC, 2002.
References
• A. Sinha, “Linear Systems: optimal and Robust Control”, CRC, 2007.
• B.D.O. Anderson and J.B. Moore “Optimal Control: Linear Quadratic Methods”, Dover, 2007.
Planned learning activities and teaching methods

Students are taught the course through lectures (3 hours per week) in classrooms or lectures theatres, by means of traditional tools or using computer demonstration.

Auditory exercises, where examples regarding matter represented at the lectures, are solved and further, questions related to particular open-ended topic issues are compiled by the students and answered, during the lecture or assigned as homework.

Topic notes are compiled by students, during the lecture which serve to cover the main issues under consideration and can also be downloaded from the lecturer’s webpage. Students are also advised to use the subject’s textbook or reference books for further reading and practice in solving related exercises. Tutorial problems are also submitted as homework and these are solved during lectures or privately during lecturer’s office hours. Further literature search is encouraged by assigning students to identify a specific problem related to some issue, gather relevant scientific information about how others have addressed the problem and report this information in written or orally.

Students are assessed continuously and their knowledge is checked through tests with their assessment weight, date and time being set at the beginning of the semester via the course outline.

Students are prepared for final exam, by revision on the matter taught, problem solving and concept testing and are also trained to be able to deal with time constraints and revision timetable.

The final assessment of the students is formative and summative and is assured to comply with the subject’s expected learning outcomes and the quality of the course.

Assessment methods and criteria
 Assignments 40% Final Exam 60%
Language of instructionEnglish
Work placement(s)NO