19-02-2013, 04:34 PM
Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method
Parameter estimation.pdf (Size: 986.54 KB / Downloads: 48)
ABSTRACT
We study the parameter estimation of a nonlinear chaotic system, which can be essentially formulated as a multidimensional
optimization problem. In this paper, an orthogonal learning cuckoo search algorithm is used to estimate
the parameters of chaotic systems. This algorithm can combine the stochastic exploration of the cuckoo search and
the exploitation capability of the orthogonal learning strategy. Experiments are conducted on the Lorenz system and
the Chen system. The proposed algorithm is used to estimate the parameters for these two systems. Simulation
results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm
optimization and the genetic algorithm when considering the quality of the solutions obtained.
Introduction
As the quintessence of a nonlinear system, chaos
is a bounded unstable dynamic behavior that exhibits
sensitive dependence on the initial conditions and includes
infinite unstable periodic motions.[1] Chaos has
been applied in many academic and engineering fields,
such as communication, economic systems, and optimization.
During the past decade, significant progress
on tackling the parameters of chaotic systems has
been made. In the real world, the parameters may
be difficult to determine due to the complexity of the
chaotic systems. Therefore, the parameter estimation
for a chaotic system has become an important issue
of nonlinear science. So far, different kinds of classical
techniques have been developed to handle these
problems.[2−7] Among them, the meta-heuristic based
method, such as the genetic algorithm (GA), the particle
swarm optimization algorithm (PSO), and the differential
evolution algorithm (DE), may be one of the
most popular methods, which formulates the problem
as a multi-dimensional optimization problem.
OLCS algorithm
In this section, we discuss how to integrate the orthogonal
learning strategy into the standard CS algorithm.
The orthogonal design[12] has been used to produce
all possible combinations of levels for a complete
factorial experiment. The basic idea of the orthogonal
design is to utilize the properties of the fractional
experiment to efficiently determine the best combination
of levels. Consider a system whose cost depends
on K factors and each factor can take one of Q levels.
To find the best level for each factor, experiments
for all combinations of factor levels should be done to
choose the best one if K and Q are small. Obviously,
the number of all combinations is QK. However, it
is not efficient to test all combinations of factor levels
if K and Q are large.
Conclusion
In this paper, a novel evolutionary algorithm, the
orthogonal learning cuckoo search algorithm, is used
for the parameter estimation of the chaotic system.
A new search strategy based on the orthogonal learning
strategy is used to enhance the exploitation ability
of the basic cuckoo search algorithm. This new
algorithm is very simple in structure and easy in application.
To verify the performance of the OLCS, the
algorithm is employed to estimate the parameters of
two chaotic dynamical systems. The experimental results
show that the OLCS can identify the parameters
of the Lorenz and the Chen systems more accurately,
more rapidly, and more stably than the CS, the PSO,
and the GA. To the best of our knowledge, this is the
first report using the improved cuckoo search algorithm
to estimate the parameters of a chaotic system.
The orthogonal learning cuckoo search algorithm can
be applied to other chaotic systems, the OLCS can be
a promising tool for various numerical optimization
problems in physics.