Lecture Plan

IIA2217 System Identification and Optimal Estimation

Week nr. Date Topics
9.1. 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 1Exercise 1.        Solution 1.      Matlab script for solution of the numerical part of exercise

Video Lectures:  Introduction

 16.1 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

                           2019 Lecture2: Problem description

Note: A link between impulse responses and discrete z-plane (or q-plane) transfer function models mentioned, as in in Ch. 2.3.7 in MPC_lect_notes

PCA, PCR og SVD. System identification of steady state systems. The Least squares (LS) method. Partial Least Squares (PLS) regressjon.

Lecture 3: OLS, PCA and SCD, PCR
Exercise 3: Exercises 8 and 7 in Note

Video Lectures: Lecture3a  Lecture3b


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

Video Lectures: Lecture 4a  Lecture4b
6.2 Identification of combined deterministic and stochastic systems.

Week 6. Basically computation of B and E. Week 7 basically how to handling noisey data. Subspace system identification. Litle 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





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 sys id of Kalman filer..", Lemma 3.9, page 15 and Ch 5. Se item 5 in syllabus list and mic-journal paper: http://www.mic-journal.no/ABS/MIC-2009-2-3.asp

Video Lecture: Lecture6a
Lecture 6 Lecture6b (Closed Loop Subspace ID)
                          Remark: Unfortunately without sound records.
                          Other videos: Se link

 20.2 State estimation and the kalman filter for linear systems. Innovations formulations and apriori-aposteriori 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
                          Lecture7_2019 (Continuos Kalman filter, Ch.2.2)



Prof of equation for kalman gain matrix.

Video Lecture: Lecture8

Exercise: Calculating the 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 mic-journal paper

MATLAB: Kalman filter example: main_ex_march6.m

10 7.3 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)
11 14.3 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.

12 21.3 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

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   Prediction error methods. More about polynomial models, ARX, OE, BOX-Jenkins etc. SS-PEM Toolbox for MATLAB, Section 12.5 in lecture notes linex2n2.m. D-SR Toolbox for MATLAB
13-14   Easter

 4.4 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 m-file: main_rols_ex.m , prbs1.m


Input and Output Model structures (polynomial models), Section 3,
ARX, ARMAX models etc.

16 18.4

Topics for Lecture14:

How to handle trends.Ch.9

Model validation.Ch.10

Input experiment design. Ch. 11

The above chapters is in the subspace lecture notes.


16 20.4 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 m-file: hank_m.m

Quote from Ljung (1999): "A high order ARX model is capable of approximating any linear system arbitrarily well."

3) Identification of non-linear systems. reformulating as a linear regression problem. Lecture notes.

17 25.4 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

Faglærer: Dr. ing., 1. amanuensis David Di Ruscio                             

Oppdatert 5.01.2018 av david.di.ruscio@usn.no