Journal
NONLINEAR DYNAMICS
Volume 67, Issue 2, Pages 1387-1395Publisher
SPRINGER
DOI: 10.1007/s11071-011-0075-6
Keywords
Fractional-order system; Approximation method; CFE; Particle swarm optimization; Chaotic optimization
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In this paper, a rational approximation me-thod is proposed for the fractional-order system using the particle swarm optimization (PSO). Firstly, the approximation method for the fractional-order operator is studied, because a fractional-order system consists of many fractional-order operators. The coefficients of the transfer function are calculated using PSO with a fitness function under the continued fraction expansion (CFE) framework in the frequency domain. The average velocity of the particle swarm is defined to reflect the real state of particle swarm. To improve the global optimization and achieve a more satisfactory fitting result, comparing with the linear PSO, the chaotic optimization is combined with PSO. The numerical examples of fractional-order systems demonstrate the effectiveness of this method.
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