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tem must be observable, which means that certain
states of the system must be measurable.
LQ approach requires a linear model of the sys-
tem, which is convenient in terms of the design pro-
cess. But in the case of highly nonlinear systems, they
provide less accurate estimations. LPV framework al-
lows integrating a set of linear models to cover the
whole nonlinear dynamics of the considered system,
see (Kang et al., 2018),(Breschi et al., 2020). The
advantages of the model-based methods include that
they can provide theoretical guarantees. However, the
efficiency and accuracy of these methods are signif-
icantly influenced by the modeling process and the
accuracy of the yielded mathematical model. In addi-
tion, the effects of changing parameters must be taken
into account to avoid performance degradation.
The second group of methods consists of solu-
tions, which do not require a nominal model of the
system, such as machine learning-based, and data-
based approaches. In (Du et al., 2010) a neural
network-based solution is presented for estimating the
side-slip of the vehicle. Pace regression can also
be used to determine the side-slip angle as proposed
in (Fenyes et al., 2018). The advantage of these
solutions is that the lack of the modeling process
makes the design process easier, and also the non-
linear and uncertain effects can be handled more ef-
ficiently. However, these methods cannot provide
stability guarantees, which are essential for safety-
critical applications. There are other solutions, which
aim to combine the classical and non-model-based ap-
proaches to eliminate their individual drawbacks. For
example, in (Zhang et al., 2021) a method is proposed,
which uses a Kalman filter and a neural network to
compensate the effect of the possible GPS signal loss.
During the last decade, a new tool came up to ef-
ficiently solve modeling-related problems, called the
ultra-local model-based approach (Fliess and Join,
2013). The motivation behind the original structure
is to approximate the system in the given operating
point. This means that the nonlinearities and uncer-
tainties can be handled using the ultra-local model.
However, the original concept has been proposed for
a control system, and several works have been pub-
lished in the field of observer design. In (Al Younes
et al., 2015) a nonlinear observer method is proposed
for aerial vehicles using the combination of the ultra-
local model-based technique and a Thau observer de-
sign.
This paper aims to combine a linear observer de-
sign method for lateral velocity estimation with the
results of the ultra-local model-based approach using
real test datasets. The original structure is modified
to take into account a priori knowledge of the system.
The modified structure is called the error-based ultra-
local model (Heged
˝
us et al., 2022). Then, the whole
design process is carried out for a vehicle model with
a nominal parameter set. The advantage of the com-
bined solution is that by using the ultra-local model-
based part of the algorithm, the differences between
the nominal model and the real system can be han-
dled effectively. The proposed algorithm is tested on
real measurement data with different test scenarios.
The test scenarios have been carried out on ZalaZone
proving ground using a Lexus RH450 test vehicle.
The paper is structured as follows: Section 2
presents the error-based ultra-local model and gives
a short introduction to LQ observer design, then de-
tails the combined design approach. In section 3, the
vehicle-oriented example is presented including the
main steps. The effectiveness of the proposed algo-
rithm is demonstrated in the vehicle simulation soft-
ware, CarSim and using real test measurements in
Section 4 . Finally, the conclusion of the paper is sum-
marized in Section 5.
2 OBSERVER DESIGN USING
ULTRA-LOCAL MODEL
2.1 Error-Based Ultra-Local Model
The core idea of the error-based ultra-local model is
to create two ultra-local models: First one is com-
puted from the measured signals, second one is de-
rived from reference signals. Then, the error-based
ultra-local model (∆
nom
) is calculated as the deviation
of two ultra-local models, see (Fenyes et al., 2022):
y
(ν)
= F + αu (1a)
y
(ν)
re f
= F
nom
+ αu
nom,re f
(1b)
y
(ν)
− y
(ν)
re f
| {z }
e
(ν)
= F − F
nom
| {z }
∆
nom
+αu − αu
nom,re f
| {z }
α ˜u
(1c)
e
(ν)
= ∆
nom
+ α ˜u (1d)
where F is the ultra local model, u control signal, y
measured output, ν order of derivative, α denotes a
free tuning parameter, y
re f
is the reference output sig-
nal, u
nom,re f
denotes the referene control input The
reference signal y
re f
and the corresponding reference
input signal, u
nom,re f
.
Finally, the additional control input ( ˜u), which
compensates the unmodelled dynamics of the system,
can be computed as:
˜u =
−∆
nom,est
α
, (2)
ICINCO 2023 - 20th International Conference on Informatics in Control, Automation and Robotics
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