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Coevolutionary Algorithm for Multivariable Discrete Linear
Time-variant System Identification
Alexander E. Robles and Mateus Giesbrecht
School of Electrical and Computer Engineering, University of Campinas, Av. Albert Einstein 400, Campinas - SP, Brazil
Keywords:
Evolutionary Algorithms, Coevolutionary Algorithms, System Identification, Time-variant System Identifica-
tion.
Abstract:
A significant part of the works in system identification is focused on time-invariant dynamic systems. How-
ever, most of systems in the real applications have nonlinear and time variant behavior. In this paper, we
present a multivariable time-variant identification method based on a paradigm in the field of evolutionary
algorithms: The coevolutionary algorithm. This new method focuses on the relationship between the fitness of
an individual in relation to the fitness of the other individuals (or group of individuals), based on the principle
of the selective pressure, that is part of the evolutionary process. A brief comparison between a multivariable
deterministic identification method MOESP-VAR and the proposed coevolutionary method is shown. From
the results it is possible to notice that the proposed method presents an accuracy higher than the obtained with
the deterministic identification method.
1 INTRODUCTION
System identification consists on finding the math-
ematical models that can describe dynamic systems
behavior, from observed input-output data (Ljung,
1999). A significant part of activities and researches
in system identification focuses on time-invariant dy-
namic systems. However, there are innumerable sys-
tems in nature that are multivariable with nonlinear
and time-varying behavior. To deal with last problem,
many of the time-varying systems are approximated
by linear time-invariant systems, as long as these sys-
tems vary slowly (Tamariz et al., 2005). In some cases
these approximations cannot describe the real variant
system behavior, so that the magnitude of the error be-
tween output data and output model is considerable.
The main focus of this paper is to present an
evolutionary method to identify multivariable time-
varying system (MTVS). For decades evolutionary
algorithms (EAs) have been applied in optimization
problems with successful results. Moreover, system
identification area had one of its first applications in
(Rodrigues-Vasquez and Fleming, 2004) when a clas-
sical genetic algorithm is applied to identify the pa-
rameters of the transfer function of a two masses res-
onant system. In (Wakizono and Uosaki, 2006) an ap-
proach for identifying linear and non-linear systems
based on CLONALG algorithm (De Castro and Von
Zuben, 2002) was proposed. Other recent work is
(Giesbrecht and Bottura, 2015), in which an immuno-
inspired algorithm was develop to identify MTVS. In
that reference, the MTVS identification problem is
defined as an optimization problem, where a search
space is created by all possible matrices quadru-
ples A,B,C, D that represent the MTVS in state-space
model for a given time interval. Furthermore, each
state-space model is seen as a point that minimizes the
error between the system and the model outputs to the
same input signal. In this paper, those principles were
used to develop the coevolutionary algorithm (COEA)
that can be applied to MTVS identification problem.
In this work, some comparisons are made between
implemented COEA and deterministic method called
MOESP-VAR (Tamariz et al., 2005), based on Multi-
variable Output-Error State sPace (MOESP) (Verhae-
gen and Dewilde, 1992). A genetic algorithm (GA)
also was implement using the same parameters and
operators used for COEA, but the populations do not
evolve together. Trying to show the effectiveness of
evolutionary processes, it was developed a random
search (RS), that performs a searching without any
evolutionary intelligence behind.
The paper is organized as follows. In the next sec-
tion, subspace methods for system identification are
introduced. In the section 3, the coevolutionary algo-
rithms are briefly detailed. Section 4 describes COEA
to identify MTVS, where the coevolution is the main
topic. In the section 5 the results of the application
290
Robles, A. and Giesbrecht, M.
Coevolutionary Algorithm for Multivariable Discrete Linear Time-variant System Identification.
DOI: 10.5220/0006907602900295
In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2018) - Volume 1, pages 290-295
ISBN: 978-989-758-321-6
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