MSc in Electrical Engineering

Course Information Package

Course Unit TitleESTIMATION THEORY
Course Unit CodeAEEE555
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. Analyze Functions of Random Variables with reference to joint distributions and densities, and define Random Vectors, Covariance and Correlation.
  2. Estimate unknown constants from redundant measurements using least squares estimation.
  3. Define Random Processes and Introduce the Markov Process, the Wiener-Levy process and White Noise.
  4. Introduce Second Order Processes and Calculus in the mean square sense.
  5. Study Solutions of Stochastic Differential Equations using the Ito Integral.
  6. Formulate the Linear Quadratic Control Problem.
  7. Design Linear Quadratic Regulators.
  8. Use Stochastic Dynamic Programming to investigate optimal linear quadratic control laws for continuous time linear stochastic systems.
  9. Design state estimators for continuous time control systems (Kalman-Bucy filter).
  10. Perform stability analysis on stochastic differential equations.
Mode of DeliveryFace-to-face
PrerequisitesNONECo-requisitesNONE
Recommended optional program componentsNONE
Course Contents

Introduction to stochastic systems and mathematical preliminaries: Probability and random processes. Random vectors. Conditional expectations. Second order processes and calculus in mean square. Stochastic differential equations. Markov processes. Wiener-Levy process. White noise. Ito Integrals and solution of stochastic differential equations.

 

Continuous time linear stochastic control systems: Analysis of causal LTI systems. LQ control problem. Optimal control of continuous time linear stochastic systems. Stochastic dynamic programming. Kalman-Bucy filter. Optimal prediction and smoothing. The separation principle. Stability analysis of stochastic differential equations. Stability of deterministic systems.

Recommended and/or required reading:
Textbooks
  • R. F. Stengel, Optimal Control and Estimation, Dover Publications, 1994.
References
  • Anderson, B., and Moore, J., Optimal Control: Linear-Quadratic Methods, Prentice Hall, 1990.
  • Athanasios Papoulis, S. Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill Science, 2001.
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
Tests30%
Assignments10%
Final Exam60%
Language of instructionEnglish
Work placement(s)NO