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System Modeling and Identification
System modeling is interdisciplinary study for models’ use for conceptualizing
and constructing the systems within IT and business development. System modeling’s
common type is the function modeling, which has specific techniques like IDEF0 and
Functional Flow Block Diagram. Such models could be extended by using functional
decomposition. Statistical models are used by system identification’s filed for building
dynamical systems’ mathematical model from the measured data (Yang et al. 2014).
Experiments’ optimal design is included in the system identification for getting efficiently
the informative data to fit such models along with the model reduction. Common
approach is starting from the measurements of system’s behavior as well as external
influences, along with attempt in determining mathematical relation among them.
Dynamical mathematical model is dynamic behavior’s mathematical description for a
process or a system in frequency or time domain.
System identification includes building dynamical systems’ mathematical models
from the experimental data. This methodology was developed to design control systems
based on model. Estimation of parameter is at heart of several applications of signal
processing which aims in extracting information from the signals such as sonar, radar,
speech, biomedical signals and communication. Identification methods and dynamical
models play an essential role in many disciplines like signal processing, economics,
physics, seismology, ecology, medicine, automatic control and physics (Baur et al.
2014). Systems of real life are nonlinear and time varying in nature, there are two other
models’ class that are used currently: nonlinear (NL) models and linear parameter-
varying (LPV) model. LPV models suit to the modeling linear time varying (LTV)

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systems, dynamics of whose are the functions of time varying measurable parameter
called scheduling variable. These could be used also to represent nonlinear systems
which are linearized with trajectory. LPV models could be seen as intermediate
descriptions among non-linear time varying models and linear time invariant (LTI)
models. The non-linear models are quite useful for several application areas which
consist of biochemical and chemical processes, pneumatic valves, systems of wireless
communications, hydraulic plants, amplifiers of high power, physiological systems,
systems of noise cancellation, loudspeakers, mechatronic systems such as robots and
vibrating structures. Models of NL are generated of concatenation of static subsystems
of NL and dynamic subsystems of LTI (El Ferik and Adeniran 2016). Linear subsystems
are parametric generally, while NL subsystems might be with memory less or with
memory. Several subsystems are connected in parallel or in series.
Multimodel framework (MMF) is approach of identification and modeling of
complicated nonlinear systems which depends on strategy of problem decomposition. In
the strategy, there is formation of global system model by set of the models that are
integrated by validity’s different degree. Several structures which includes linear,
mechanistic, nonlinear, hybrid, empirical and neutral networks are available. Gaussian
processing model could be introduced as structure of local model. The approach gives
several advantages such as ill conditioning and robustness as well as provides measure
for uncertainty in prediction (Shraim, Awada and Youness 2018). Structure of sub
models is MMF’s most flexible area, as no certain requirements are there instead of
local regime’s satisfactory approximation. The sub models could be heterogeneous or
homogeneous. Homogeneous sub models could be referred to as models of similar

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structures. Heterogeneous sub models could be referred as sub models of several
separate structures, which are used commonly within networks of local model.
Homogeneous sub models are favored mostly as their techniques for optimization and
learning are same (Kirsh and Kupriyanov 2015). Heterogeneous sub models might need
different techniques for optimization and learning that are appropriate for each sub
model. Though unlike the homogeneous sub models, these could cope with
dimensionality’s curse and are much more flexible.
Estimation of parameters of local model provided a specific model structure is
done by local learning or global learning cost function. Global learning’s objective is
minimizing error between output of system and output of multimodel. Hence, the global
learning gives estimates of parameters of local models. Global learning is perfect for
properly chosen structure of model. Though, it is difficult usually in obtaining suitable
model. Additionally, this needs huge effort of computation for huge training samples as
well as generates lesser transparent models, as each sub model could not be
separately interpreted. As alternative, it is responsibility of local learning to take care of
global learning’s disadvantages through focusing on useful local information that is
extracted from the data (Emami and Banazadeh 2016). This approach minimizes error
between output of system and outputs of every local model. Hence, this produces
parameters’ independent estimation for each sub model. Though, superior performance
is demonstrated by local learning to the global learning, this suffers from disadvantages
to discard global useful information from the data.
Efforts are made for investigating on this in several structures of multimodel. It is
observed that algorithm of combined learning over polynomial local model could be

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implemented. This algorithm combined both global as well as local cost functions for
providing tradeoff among global fitting and local interpretation (Wen et al. 2017).
Algorithm of combined learning is suited well for overlapped function of Gaussian
validity. For solving criteria of optimization, different algorithms could be used to
estimate parameters of sub models depending on sub models’ different structures. Most
used algorithm for identification is algorithm of least square (LS) or recursive version
(RLS) for models of LIP-type.
Validity computation’s determination is other challenge within interpolated MMF.
Validity function describes contributions of every local model to multimodel output s well
as allows a smooth transaction among several local models. Hence, selection of the
function could affect accuracy of representation. There are validity computation’s two
categories that could be identified. One is the prevalidity computation, in where
determination of validity could be done during partition of operating space. Computation
of it is based on strategy of selected partition. Validity could be directly employed in
estimation of parameters of local model. Other is post validity computation, which is
when there is computation of validity after identification of local models and is
independent of strategy of partition (Shukla and TK 2017). Central to these categories is
determination of vector of scheduling variable that defines multimodel system’s
operating region as well as assists in blending. Scheduling vector must be subset of
information space for reducing dimensionality’s curse. Vector’s reduced dimension
could result in decrement of accuracy as well as produces global model that is
discontinuous.

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Gaussian validity is validity function that is owing the popularity to smoothness
property. This is prevalidity computation mainly, which could be used to determine
parameters of local model. Though, this method could be used also like post validity
computation. Determination of width and center is really essential to accuracy of
identified system. For partition based on experiment, center could be chosen as
collected data’s operating point (Jihin, Kögler and Söffker 2019). However, it could be
challenging to other strategies of partition, hence several other strategies are adopted in
determination. Data’s center could be used as center of Gaussian function as well as
optimized width of function by minimization of error of mean square over training data.
In applications of nonlinear, MMF is exploited for avoiding substantial complexity
with respect to implementation and design of controller generated by theories of
nonlinear control. Multimodel controllers employ the linear control that is owing to easy
implementation as well as accessible methodologies of linear control. Control of
nonlinear system is dealt by interpolated MMF through fusion process of local
controllers that were designed previously. There is decomposition of nonlinear system
into local linear model’s set by using any strategies of partition (Fichera and Grossard
2017). Based on every local model, local controller is designed by using techniques of
linear control. In partial fusion for outputs of controllers’ local controllers’ output are
weighted, depending on each model’s contribution, for obtaining final control signal of
the system.

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References
Baur, R., Blath, J.P., Bohn, C., Kallage, F. and Schultalbers, M., 2014. Modeling and
identification of a gasoline common rail injection system (No. 2014-01-0196). SAE
Technical Paper.
El Ferik, S. and Adeniran, A.A., 2016. Modeling and identification of nonlinear systems:
A review of the multimodel approach—part 2. IEEE Transactions on Systems, Man, and
Cybernetics: Systems, 47(7), pp.1160-1168.
Emami, A. and Banazadeh, A., 2016. Control oriented modeling and identification of
nonlinear systems. In Applied Mechanics and Materials (Vol. 841, pp. 330-337). Trans
Tech Publications Ltd.
Fichera, F. and Grossard, M., 2017. On the modeling and identification of stiffness in
cable-based mechanical transmissions for robot manipulators. Mechanism and Machine
Theory, 108, pp.176-190.
Jihin, R., Kögler, F. and Söffker, D., 2019, June. Data Driven State Machine Model for
Industry 4.0 Lifetime Modeling and Identification of Irrigation Control Parameters.
In 2019 Global IoT Summit (GIoTS) (pp. 1-6). IEEE.
Kirsh, D.V. and Kupriyanov, A.V., 2015. Modeling and identification of сentered crystal
lattices in three-dimensional space. In Proceedings of Information Technology and
Nanotechnology (ITNT-2015), CEUR Workshop Proceedings (Vol. 1490, pp. 162-170).

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Shraim, H., Awada, A. and Youness, R., 2018. A survey on quadrotors: Configurations,
modeling and identification, control, collision avoidance, fault diagnosis and tolerant
control. IEEE Aerospace and Electronic Systems Magazine, 33(7), pp.14-33.
Shukla, V.V. and TK, K.N., 2017. Modeling & Identification of High Performance Aircraft
in Frequency Domain. Journal of Mechanical and Aeronautical Engineering
Research, 1(1), pp.1-8.
Wen, L., Wang, X., Dong, Z. and Chen, H., 2017, November. Jointly modeling intent
identification and slot filling with contextual and hierarchical information. In National
CCF Conference on Natural Language Processing and Chinese Computing (pp. 3-15).
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Yang, S., Wu, M., Yao, X. and Jiang, J., 2014. Load modeling and identification based
on ant colony algorithms for EV charging stations. IEEE Transactions on Power
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