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The Application of Evolutionary Algorithm for the Linear Dynamic
System Modelling
Ivan Ryzhikov and Eugene Semenkin
Institute of Computer Sciences and Telecommunication, Siberian State Aerospace University,
Krasnoyarskiy Rabochiy ave., 31, Krasnoyarsk, 660014, Russia
Keywords: Linear Dynamic System, Linear Differential Equation, Evolutionary Strategies, Parameters Identification
Problem, Structure Identification.
Abstract: The approach to dynamic system modelling in the linear differential equations form is presented. The given
approach fits the identification problems with the system output observations sample and the input sample
even if the output data is distorted by a noise. The structure and parameters identification problem is
reduced to a global optimization problem, so that every solution consists of the model structure and its
parameters. This allows searching the analytical model in the ordinary differential equation form with any
limited order. The analytical model delivers a special benefit in its further use in the control and behaviour
estimation problem.
1 INTRODUCTION
There are many different approaches to make a
model of the dynamic system. The identification
task itself depends on the given structure and the
parameters estimation special technique. Also, the
practice need tends one to make the model in an
analytical form so it would be easier to find out a
control function or predict the system behaviour
with different input functions or initial points. We
can approximate the system output and use the
special technique to define its unit step function
reaction or we can make the model in a dynamic
form. The model that was built as an approximation
with a function base is not as useful and flexible as a
dynamic model. Moreover, the task would be
reduced to the enumerative technique for the
different combination of functions, while we do not
know, for example, the order of equation or
multiplicity of characteristic equation roots. In the
article (Janiczek, Janiczek, 2010) we can see an
identification method in terms of fractional
derivatives and the frequency domain. The
information about the plant is taken from the given
frequency domain and not from the output
observations that could be distorted. Also, special
control and regulation methods are required to the
model in fractional derivatives. We can use
stochastic difference equations (Zoteev, 2008), and
build a model using the output observations,
observations of the reaction on the step excitation.
This approach is partially parameterized, i.e., the
order and functional relation between the system
state and previous states are unknown. In (Parmar,
Prasad, Mukherjee, 2007), the dynamic system
approximation with the second order linear
differential equations is examined. The coefficients
are determined with the genetic algorithm. In this
paper, there is the description of the structure and
parameters identification task solving by means of
the reduction of the identification task to a real value
optimization problem with the modified
evolutionary strategies method. The algorithm
workability and usefulness are demonstrated on the
real identification problem.
The rest of the paper is organised in the
following way. In Section 2 we describe the problem
statement of the system structure and parameters
estimation, in Section 3 the modified hybrid
evolutionary strategies algorithm for the ordinary
differential equation identification is described, in
Section 4 we fulfill modelling the chemical reaction
with described approach, and in Conclusion we
summarise our results.
234
Ryzhikov I. and Semenkin E..
The Application of Evolutionary Algorithm for the Linear Dynamic System Modelling.
DOI: 10.5220/0004060402340237
In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2012),
pages 234-237
ISBN: 978-989-8565-20-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)