Single-Course English 5 ECTS

Stochastic Adaptive Control

Overall Course Objectives

A student who has successfully completed the course will be able to do the following.
1. Model and control dynamical systems that are subject to unknown and/or time-varying disturbances and variations in parameter values.
2. Identify stochastic systems (specifically, their parameter values) based on measurements.
3. Develop adaptive control methods which can mitigate the effects of the unknown/time-varying disturbances and/or parameter values.

Learning Objectives

  • Describe a physical process using an internal (state space) or external (ARMAX) model.
  • Linearize and discretize nonlinear continuous-time models.
  • Analyze internal and external models (e.g., using Lyapunov equations).
  • Monitor the state of a system (e.g., using a Kalman filter).
  • Control a process (e.g., using a linear quadratic regulator (LQR)).
  • Identify a system (i.e., the parameter values in a model of the system).
  • Monitor unknown time-varying disturbances or parameters (online system identification).
  • Mitigate the effects of unknown variations in disturbances and parameter values using adaptive control.
  • Describe the key aspects of the methods presented during the course, their main purpose, and the underlying assumptions.
  • Account for the underlying mathematics of the methods, e.g., key steps in the derivation. (For instance, the projection theorem is a key step in the derivation of the Kalman filter.)
  • Modify existing methods and derive new methods for systems not presented in class. (For instance, apply the Kalman filter and LQR to a system with correlated process and measurement noise.)

Course Content

In this course, we combine analysis of stochastic systems with controller design, state and parameter estimation, and experiment design (both offline and online) to create adaptive control algorithms that can mitigate the effect of time-varying parameters and unknown disturbances.

We will focus on linear discrete-time state space models and ARMAX models. For the state space models, we will consider the Kalman filter, the linear quadratic regulator (LQR), the linear quadratic gaussian (LQG) regulator, and generalized predictive control. Furthermore, we will consider the extended Kalman filter for parameter estimation. For the ARMAX models, we will consider extended least-squares, maximum likelihood, and prediction error methods (as well as their recursive variants) for parameter estimation and generalized minimum variance and generalized predictive algorithms for control. Finally, we will use various approaches for creating informative experiments and validating the identified models before combining all of the above into stochastic adaptive control algorithms which repeatedly identify the system and updates the designed controller accordingly.

Recommended prerequisites

02402/02405/34721/28150/02417, Introductory course in statistics (02402) or probability theory (02405) and in control (34721 / 28150) or time series analysis (02417).

Teaching Method

Lectures and exercise sessions.



In this course, control theory is combined with control design, statistics, probability theory, and optimization methods. The course is related to other advanced courses in control.

See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 02421
Course type Candidate
Semester start Week 5
Semester end Week 19
Days Tues 8-12

7.500,00 DKK