Identification of nonlinear systems using adaptive variable-order fractional neural networks (Case study: A wind turbine with practical results)

In this paper, a Variable-Order Fractional Single-layer Neural Network (VOFSNN) and a Variable-Order Fractional Multi-layer Neural Network (VOFMNN) are proposed to identify nonlinear systems assuming all the system states are measurable. Fractional Lyapunov-like approach and Gronwall-Bellman integral inequality are employed to prove stability and asymptotic stability conditions of the identification error dynamics. A set of novel stable learning rules for the fractional order, the hidden layer weights and the output layer weights are derived to update the proposed VOFSNN and VOFMNN parameters. The proposed methods capabilities are evaluated and confirmed by the practical data gathered from a wind turbine under operation in a wind farm.