Abstract
In this work, we study an application of fractional-order Hopfield neural networks for optimization problem solving. The proposed network was simulated using a semi-analytical method based on Adomian decomposition,, and it was applied to the on-line estimation of time-varying parameters of nonlinear dynamical systems. Through simulations, it was demonstrated how fractional-order neurons influence the convergence of the Hopfield network, improving the performance of the parameter identification process if compared with integer-order implementations. Two different approaches for computing fractional derivatives were considered and compared as a function of the fractional-order of the derivatives: the Caputo and the Caputo–Fabrizio definitions. Simulation results related to different benchmarks commonly adopted in the literature are reported to demonstrate the suitability of the proposed architecture in the field of on-line parameter estimation.
Highlights
The problem of system identification is ubiquitous in different research fields ranging from biology to engineering applications
It is well established that Hopfield neural networks (HNNs) [17,18] can be used to solve optimization problems, including parameter estimation in the context of system identification [9]
A comprehensive study of the problem of using HNNs for on-line parameter estimation has been provided in [4]. While these studies are based on integer order real neuron models, in our work we examine a generalization of HNNs which dynamic can be described by fractional-order differential equations [10] and, for the first time, we apply them to parameter estimation problems
Summary
The problem of system identification is ubiquitous in different research fields ranging from biology to engineering applications. The Caputo and the Caputo–Fabrizio definitions were applied to develop the proposed fractional-order HNN and compared on two different cases of study commonly adopted in the literature. The former is related to the estimation of the parameter in the well-known Lorenz system that exhibits a chaotic behaviour [28]. It has been used as testbed by Lazzs and coauthors in [26] to evaluate the performances of parameter estimation methods based on swarm intelligence The latter case of study is related to a mechanical two-cart system, adopted in [4] to evaluate the identification performance of an integer-order HNN.
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