Week
nr. 
Date 
Topics 
2 
10.112.1 
Introduction to system
identification. Notations, state space models,
realization theory, hankel matrix, impulse response
matrices. Identification of impulse responses.
Hankel matrices and system order.
Lecture 1: Lecture notes Ch.1, Section 2.2.5,
Exercise 1. Exercise 1.
Solution
1. Matlab script for
solution of the numerical part of exercise
Lecture notes on Finite Impulse Response (FIR)
models
Video Lectures: Introduction
Realization_theory
prbs1.m
for experiment design (download here or on
exercise page)
MATLAB example main_ex1_lecture1.m

3 
17.119.1 
Realization theory.
Singular value decomposition (SVD). Different state
space model realizations; output normal, input
normal and balanced realizations. System
identification of autonomeous systems.
Lecture 2: Lecture notes: Ch. 1, Sec. 2.2.5, Sec.
4.10
Exercise 2: Taken as Task 1 in exercises.
Video Lectures:
Lecture2a
Lecture2b
Realization_etc
Sid_autonomeous_syst
SVD_div
2019 Lecture2:
Problem description
Lecture notes on Finite Impulse Response (FIR)
models
Note: A link between impulse responses and
discrete zplane (or qplane) transfer function
models mentioned, as in in Ch. 2.3.7 in MPC_lect_notes
MATLAB
example: Realization theory

4 
24.126.1 
PCA, PCR og SVD. System
identification of steady state systems. The Least
squares (LS) method. Partial Least Squares (PLS)
regression. PLS only mentioned and not in details.
Lecture 3: OLS,
PCA and SVD, PCR
Exercise 3: Exercises 8 and 7 in Note
Video Lectures: Lecture3a
Lecture3b
Lecture3_ols
Lecture3_ols_b
Lecture3_PCA

5 
31.12.2 
Identification of
deterministic systems. Identification of system
order, the extended observability matrix of the
system and the dynamic properties, i.e.
identification of, n, O_L, A and D. Orthogonal
projection matrices.
Lecture 4: SID of deterministic systems. Autonomeous
systems intro
Exercise 4: Exercises 11 and 12
in Note Solution
proposals for Exercise11/Task 11 here: losn_oppg10.m
Video Lectures: Lecture
4a Lecture4b
Lect4_intro
Lect4_id_det_syst
Lect4_orth_pro 
6 
7.29.2 
Identification of
combined deterministic and stochastic systems.
Computation of B and E from tilde(B) matrix. How
to hande noisy data. Subspace system
identification. Little about the Kalman filter.
Lecture5: SID of the general problem, i.e.
Combined deterministic and Stochastic Systems.
Lecture notes Ch. 3, Ch. 4, Ch. 8.3.2, 8.3.4
Video Lectures: Lecture
5a Lecture5b
Lecture_combined
Lecture_Kalman_intro

7

14.216.2

Subspace identification
of combined deterministic and stochastic systems,
and identification of the innovations process and
closed loop systems.
Also theory as described previous week.
1) Closed
and Open Loop SID of Kalman Filter. Ch. 6
2) Paper, "On system identification of the Kalman
filter..", Lemma 3.9, page 15 and Ch 5 in item
5 in syllabus list and micjournal paper: http://www.micjournal.no/ABS/MIC200923.asp
Video Lecture: Lecture6a
MATLAB mfile example, main_clopid_ex1,m

89 
21.223.2
(28.21.3) 
State estimation and the
kalman filter for linear systems. Innovations
formulations and aprioriaposteriori formulation of
the kalman filter for discrete time linear systems.
Lecture notes: State estimation
and Kalman filter, Ch. 2.2, 2.6.2, 2.6.3
Video Lectures: Lecture7a
Lecture7b
Lecture_Kalman_intro
Lecture7_2019
(Continuous Kalman filter, Ch.2.2)
Example: main_oppg13_ext.m

89 
28.21.3
3.3 
Prof of equation for Kalman gain matrix.
Video Lecture: Lecture8
Exercise: Calculating the Kalman
gain matrix. (MATLAB mfile)
Simple proof of Kalman
gain matrix.
Exam 2014: Tasks 4 kalman filter. Task 5 and 6.
Susbspace SID, shift invariance principle and
feedback in data. Details in Ch. 6 in micjournal
paper
http://www.micjournal.no/PDF/2009/MIC200923.pdf
MATLAB: Kalman filter example: main_ex_march6.m

10

6.38.3 
Prof of some Kalman
filter equations. Lecture notes: State estimation
and Kalman filter, Ch. 2.6.2, 2.6.3.
State estimation and the Kalman filter for non
linear systems, the Extended Kalman Filter (EKF). Lecture notes:
Ch. 3
Video Lectures: Lecture9
(The EKF)
Lecture78_EKF 
11 
13.315.3 
Kalman filter and
introduction to prediction error methods for system
identification.
Video Lecture: Lecture10
(Introduction to PEM
Exercise : Kalman
filter exercise. Work through parts of
Kalman filter exercise 2 as described in Exercise
plan, Week 1213, with mfile solution proposals.
Demo Advanced Control IIAV3017: demo1_advanced_control.m
dlqdu_pi.m

11 
15.320.3 
Prediction error methods for system
identification, parameter estimation and Kalman
filter. Polynomial, ARMAX and state space models.
The prediction
error method and linear regression models.
Ch. 2,3, 2.3.2. (Syllabus from Item 4 in syllabus
page. )
Work out the proof of Eq.
(55) on page 11.
Video Lecture: Lecture11
Exercise: Curve fit example using MATLAB polyfit.m
and polyval.m functions to fit a polynomial to
data X and Y, and MATLAB plotting facilities. main_ex_polyfit.m

12 
20.322.3 
TOPICS
1. Prediction error methods. More about polynomial
models, ARX, OE, BOXJenkins etc. as in Sec 3 in lecture
notes. This is also the topic in Week 15.
2. SSPEM Toolbox
for MATLAB, Section 6.1 in lecture
notes.
3. A MIMO (m=2 and r=2) system with n=3 states
syntetic example. MATLAB mfiles linex2n2.m utype.m
4. Estimate State Space (SS) model using DSR Toolbox for MATLAB
and the MIMO example mentioned above.
5. EXAMPLE: SISO 1st order general linear model.
State Space model, Linear Regression model, ARMAX
and ARX models). Ch3 in syllabus
item4

13 
27.329.3 
The prediction
error method and the Ordinary Least Squares (OLS)
method. ARX models and the OLS method. Statistical
analysis of the OLS estimate. The Best Linear
Unbiased Estimator (BLUE).
The recursive OLS method, Section
7, p. 26
Video Lecture: Lecture12
Exercise: Illustration of ROLS method Ex. 7.2
with mfile: main_rols_ex.m ,
prbs1.m
MATLAB demo

13 
Easter 

14 
3.45.4 
Input and Output Model structures (polynomial
models), lecture
notes Ch.3 p. 14. ARX, ARMAX models etc.
Also same as Lecture12 Week13, the
Recursive OLS, the ROLS method.
Quote from Ljung (1999): "A high order ARX model
is capable of approximating any linear system
arbitrarily well."
A view on closed loop subspace system
identification, the DSR_e algorithm and MIC
paper.







15 
10.412.4 
Topics for Lecture14:
1. How to handle trends.Ch.9
2. Model validation.Ch.10
3. Input experiment design. Ch. 11. MATLAB
function prbs1.m to
generate Pseudo Random Binary (PRBS) input signal
experiments.
The above chapters is in the "subspace"
lecture notes.
Lecture14
Exercises: As in ExercisePlan

16 
17.419.4 
EXERCISE
1) Work with earlier exercises
2) System identification by first identification of
a higer order ARX model and following by model
reduction. MATLAB function: harxmr.m This
function is using mfile: hank_m.m
Quote from Ljung (1999): "A high order ARX model
is capable of approximating any linear system
arbitrarily well."
3) Identification of nonlinear systems.
Reformulating as a linear regression problem. Lecture notes.

17 
25.427.4 
Summing up the main
topics:
1) Realisation theory.
2) Subspace based methods for system
identification.
3) Optimal state estimation and the Kalman
Filter.
4) Prediction error methods for system
identification.
Summary on Web 


