Adaptive and Robust Control

Course Description

Introduction: How to control time varying systems. Examples of time varying systems. Difference between adaptive and robust control.Adaptive control structures (gain scheduling, with the reference model (MRAS). Selftuning regulator. Recursive least squares method and extended recursive least squares method in parameter identification. Stability, convergence and robustness. Design of STR by pole/zero placement. Stochastic adaptive control: minimum variance (MV). Robust control. Introduction. Uncertainty clasess. Structured and unstructured uncertainities. Small gain theorem. Robust stability analysis. Kharitonov s theorem.

General Competencies

Students will learn how to control time varying systems. Students will acquire the basic concepts of adaptive and robust control.

Learning Outcomes

  1. identify systems suitable for the application of adaptive management
  2. define a suitable method for controlling systems with variable parameters
  3. distinguish processes suitable for the application of MRAS and self tuning regulator
  4. apply methods of adaptive control model reference
  5. apply a recursive method of identification
  6. apply the pole placement synthesis method
  7. identify the types of parameters uncertainty
  8. analyze the robust stability using the small gain theorem and the theorem Kharitonova

Forms of Teaching


Lectures 2 hours per week


Home works, Midterexam, Final exam - written form, Oral final exam.


After the lectures.



Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Homeworks 0 % 30 % 0 % 10 %
Mid Term Exam: Written 0 % 25 % 0 %
Final Exam: Written 0 % 25 %
Final Exam: Oral 20 %
Exam: Written 0 % 40 %
Exam: Oral 50 %

Week by Week Schedule

  1. Introductory course considerations: overview of teaching units, the organization of the teaching and examination. Review of methods of adaptive management. Examples.
  2. Gain scheduling adaptive control.
  3. Model reference adaptive control with parameter adatpation.
  4. Model reference adaptive control with signal adatpation.
  5. Sliding mode adaptive control.
  6. Methods of self tuning adaptive control. Identification of the model.
  7. Identification of parameters (dynamics, persistence, minimum square, bias)
  8. Midterm exam.
  9. The minimum variance adaptive control.
  10. LQG adaptive control.
  11. Self tuning adaptive control based on pole placement method. The distinction between the application of adaptive and robust control.
  12. Robust Control. Structured and unstructured uncertainties.
  13. Application of the small gain theorem.
  14. Application of the Kharitonov theorem.
  15. Final exam.

Study Programmes

University graduate
Control Engineering and Automation (profile)
Specialization Course (2. semester)


Z. Vukić (2000.), A Tutorial on Adaptive Control: The Self-tuning Approach, IEEE Southeastcon
P. E. Wellstead; M. P. Zarrop (1991.), Self-tuning Systems - Control and Signal Processing, John Wiley & Sons.
K.J. Astrom; B. Wittenmark (2008.), Adaptive Control, Dover Publication
S. Sastry; M. Bodson (1989.), Adaptive Control: Stability, Convergence, Robustness, Prentice Hall Inc.

Grading System

ID 34367
  Summer semester
L3 English Level
L1 e-Learning
30 Lecturers
0 Exercises
0 Laboratory exercises


87,5 Excellent
70 Very Good
67,5 Good
50 Acceptable