IST/ISR
floating ball setup
MSc dissertation
proposal 2014/2015
Introduction:
As
noted by Fliess et al, in the work named
"Non-linear estimation is easy"(2008), knowing the state of a continuous
system and its derivatives as functions of the control and output variables, is
equivalent to know the system itself. Commonly, one has sensors giving
observations of the state but not of its time derivatives. In order to identify
the system, one can than follow a system discretization
approach, as proposed e.g. by Lennart Ljung or, more recently, try to estimate directly the
derivatives using filtering kernels. We propose following the later approach,
i.e. considering very simple, non-causal, first order, difference kernels to
estimate the derivatives.
Objectives:
Given
a nonlinear Single-Input-Single-Output (SISO) system, identify its parameters
considering that the system is defined as a polynomial model in the state and
the input variables. Explore simple derivative approximations to identify the
system using few computations.
Detailed
description:
Considering
a SISO dynamic system model, having x as the system state, u the control input,
y the measurements and f, g denoting nonlinear system and measurement
functions, i.e. dx/dt(t) = f(x(t), u(t); p), and y(t)= g(x(t), u(t); p) our
objective is to identify the system parameters, p usually unknown, or
inaccurately known, in real systems. The functions f and g are assumed to be
polynomials in x and u.
Work-proposal
detailed steps:
-
Create a Matlab/Simulink nonlinear SISO system, and
use it to test the system identification methodology
-
Compare the identification methodology with gold standard methodology by Fliess et al. [Fliess08]
-
Test the identification methodology on a real system
References:
[Fliess08]
Michel Fliess, Cedric Join, Hebertt
Sira-Ramirez, ”Non-linear estimation is easy”, Int.
Journal of Modelling,
Identification and Control, V4n1, pp12-27, 2008.
[Ljung99]
Lennart Ljung, ”System Identification - Theory For the User”, 2nd ed, PTR Prentice Hall,
N.J.,
1999.
[Zehetner07]
J. Zehetner, J. Reger, M.
Horn, ”A Derivative Estimation Toolbox based on
Algebraic Methods — Theory and Practice”. IEEE 2007 Multi-conference
on Systems and Control (MSC 2007).
Requirements
(grades, required courses, etc):
-
Expected
results:
At
the end of the work, the students will have enriched their experience in
nonlinear system identification.
Place
for conducting the work-proposal:
ISR
/ IST
More MSc
dissertation proposals on Computer and Robot Vision in:
http://omni.isr.ist.utl.pt/~jag