Parameter Estimation for Chaotic Fractional Systems by Using the Locust Search Algorithm

Abstract

Due to its multiple applications, parameteridentification for fractional-order chaotic systems hasattracted the interests of several research communities.In the identification, the parameter estimation processis transformed into a multidimensional optimizationproblem where fractional orders, as well as functionalparameters of the chaotic system are considered thedecision variables. Under this approach, the complexityof fractional-order chaotic systems tends to producemultimodal error surfaces for which their cost functionsare significantly difficult to minimize. Several algorithmsbased on evolutionary computation principles havebeen successfully applied to identify the parameters offractional-order chaotic systems. However, most ofthem maintain an important limitation; they frequentlyobtain sub-optimal results as a consequence of aninappropriate balance between exploration andexploitation in their search strategies. This paperpresents an algorithm for parameter identification offractional-order chaotic systems. In order to determinethe parameters, the proposed method uses theevolutionary method called Locust Search (LS), whichis based on the behavior of swarms of locusts. Differentto the most of existent evolutionary algorithms, itexplicitly avoids the concentration of individuals in thebest positions, eliminating critical flaws such as thepremature convergence to sub-optimal solutions andthe limited exploration-exploitation balance. Numericalsimulations have been conducted on the fractional-Order Van der Pol oscillator to show the effectivenessof the proposed scheme.