Adaptive and Optimal Control


Recommended prerequisite for participation in the module

Linear control theory, numerical methods, optimization theory

Content, progress and pedagogy of the module

The course purpose is to contribute to students’ attainment of knowledge and comprehension of the fundamental knowledge of advanced control with adaptive mechanisms and optimal control techniques. 

Adaptive control:

  • Introduction to adaptive control
  • Typical adaptive control principles and methods
    • Feed-forward adaptive control and feedback adaptive control
  • Feedback adaptive control
    • Gain scheduling
    • Model Reference Adaptive Control (MRAC)
      • Gradient optimization MRAC’s
      • Stability optimized MRAC’s
    • Model identification adaptive control
    • Parametric adaptive control
      • Explicit parameter adaptive control
      • Implicit parameter adaptive control
    • Multiple model adaptive control
    • Self-tuning regulators

 Optimal Control:

  • Review of optimal control principles
  • Infinite horizon optimization: Linear Quadratic (LQ) control
    • Standard problem formulation
    • Solutions and Riccati equations
    • Discrete-time  LQ control
    • Linear quadratic Gaussian (LQG)control
    •  Application examples
  • Finite horizon optimization (I): Minimum Variance Control (MVC)
    • Problem formulation for SISO systems
    • Solution and its properties
    • Generalized MVC
    • Offset problem
    • Self-tuning MVC
  • Finite horizon optimization (II): Model predictive Control (MPC)
    • Principles of MPC
    • Typical MPC schemes based on different models
    • Numerical computation algorithms
    • Nonlinear MPC
    • Commercial software and examples
  •  Adaptive MPC
    • Principles of adaptive MPC
    • Typical algorithms

Learning objectives


  • Have comprehension of the fundamental principles of typical adaptive control methods
  • Have comprehension of the fundamental principles of typical optimal control methods


  • Be able to use different adaptive and optimal control algorithms.
  • Be able to apply some typical adaptive/optimal control methods to solve some specific linear control problems under the assistance of available computation software


  • Independently be able to define and analyze scientific problems within the area of adaptive and optimal control.
  • Independently be able to be a part of professional and interdisciplinary development work within the area of adaptive and optimal control.

Type of instruction

The program is based on a combination of academic, problem-oriented and interdisciplinary approaches and organized based on the following work and evaluation methods that combine skills and reflection:

  • Lectures
  • Classroom instruction
  • Project work
  • Workshops
  • Exercises (individually and in groups)
  • Teacher feedback
  • Reflection
  • Portfolio work

Extent and expected workload

Since it is a 5 ECTS course module, the work load is expected to be 150 hours for the student



Name of examAdaptive and Optimal Control
Type of exam
Written or oral exam
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Additional information

Elective course
On this semester two courses must be chosen out of three elective courses (total: 10 ECTS).

Facts about the module

Danish titleAdaptiv og optimal regulering
Module codeN-IRS-K3-5
Module typeCourse
Duration1 semester
Language of instructionEnglish
Empty-place SchemeYes
Location of the lectureCampus Esbjerg
Responsible for the module


Education ownerMaster of Science (MSc) in Engineering (Intelligent Reliable Systems)
Study BoardStudy Board of Build, Energy, Electronics and Mechanics in Esbjerg
DepartmentDepartment of Energy
FacultyThe Faculty of Engineering and Science