Massachusetts Institute of Technology
6.435 System Identification
Prof. M. A. Dahleh
Out 04/13/1994
Problem Set No. 5
Due 04/25/1994
Reading: Chapters 9,10,11.
Do the following problems from Ljung's book:
a. 7G.3
b. 7E.6
c. 7D.1
d. 7D.5
-.
e. 7G.1 (a,b,c)
Massachusetts Institute of Technology
6.435 System Identification
Prof. M. A. Dahleh
Out 3/16/1994
Problem Set No. 4
Due 3/28/1994
Reading: Chapters 7,8.
Do the following problems from Ljung's book:
a. 7G.1
b. 7G.2 (part a)
c. 7G.7
d. 7E.2
e. 7E.3
f. 7E.4
I
'P.
Problem Set 2
6.435 System Identification
Ali J. Azarbayejani
9 October
1991
1. Nonparametric time- and frequency-domain methods.
Ljung Problem 6G.3
E GN(eiw)I
= EGN(ew)GN(eiw)
= EGN(eiW)GN(e-iW)
i
= E (Go(ew) +
K1
f.RN(W) (G (G + + RN(-W) VN(-W)
NW
d. Do your extimates change if you assumed that the system has no delays (again using
"spa" and "arx" ).
Problem 5 Repeat all of the above for a step input, again with random noise.
System Identification
6.435
SET 9
Asymptotic distribution of PEM
Munther A. Dahleh
Lecture 9
6.435, System Identification
Prof. Munther A. Dahleh
1
Central Limit Theorem
(Generalization)
Basic Theorem II:
Consider
are both ARMA processes, possibly corre
System Identification
6.435
SET 8
Convergence and Consistency
Informative Data (relation to p.e.)
Convergence to the true parameters
(role of identifiability)
Munther A. Dahleh
Lecture 8
6.435, System Identification
Prof. Munther A. Dahleh
1
Convergenc
System Identification
6.435
SET 7
Parameter Estimation Methods
Minimum Prediction Error Paradigm
Maximum Likelihood
Munther A. Dahleh
Lecture 7
6.435, System Identification
Prof. Munther A. Dahleh
1
Parameters Estimation Methods
Paradigm: Pick the para
System Identification
6.435
SET 6
Parametrized model structures
One-step predictor
Identifiability
Munther A. Dahleh
Lecture 6
6.435, System Identification
Prof. Munther A. Dahleh
1
Models of LTI Systems
A complete model
u = input
y = output
e = noise
System Identification
6.435
SET 5
Least Squares
Statistical Properties
Munther A. Dahleh
Lecture 5
6.435, System Identification
Prof. Munther A. Dahleh
1
Least Squares
Linear regressions
LS Estimates: Statistical properties
Bias, variance, covariance
System Identification
6.435
SET 4
Input Design
Persistence of Excitation
Pseudo-random Sequences
Munther A. Dahleh
Lecture 4
6.435, System Identification
Prof. Munther A. Dahleh
1
Input Signals
Commonly used signals
Step function
Pseudorandom binary se
System Identification
6.435
SET 3
Nonparametric Identification
Munther A. Dahleh
Lecture 3
6.435, System Identification
Prof. Munther A. Dahleh
1
Nonparametric Methods
for System ID
Time domain methods
Impulse response
Step response
Correlation analy
Introductory Examples
for
System Identification
Munther A. Dahleh
Lecture 2
6.435, System Identification
Prof. Munther A. Dahleh
1
Examples of Sys. Id.
Will use two systems,
Objective
Study the mechanics of sys. id.
Introduce linear regressions to minimiz
System Identification
6.435
SET 1
Review of Linear Systems
Review of Stochastic Processes
Defining a General Framework
Munther A. Dahleh
Lecture 1
6.435, System Identification
Prof. Munther A. Dahleh
1
Review
LTI discretetime systems
transfer function
Not