Online Identification of Uncertain Fractional-Order Nonlinear Systems Using a Reinforced Differential Evolution Optimizer

Abstract

Parameter identification as known as a significant issue is investigated in this paper. The research focus on online identifying unknown parameters of uncertain fractional-order chaotic and hyperchaotic systems, which shows great potential in recent applications. Up to now, most of the existing online identification methods only focus on integer-order systems, thus, it’s necessary to expand these fundamental results to uncertain fractional-order nonlinear dynamic systems and adopt an effective optimizer to deal with the model uncertainties. Motivated by this consideration, this research introduces an efficient optimizer to offline and online parameter identification of the fractional-order chaotic and hyperchaotic systems through non-Lyapunov way. For problem formulation, a multi-dimensional optimization problem is converted into from the problem of parameter identification, where both systematic parameters and fractional derivative orders are considered as independent unknown parameters to be estimated. The experimental results illustrate that SHADE is significantly superior to the other compared approaches. In this case, online identification is conducted via SHADE, the simulation results further indicate that success-history based adaptive differential evolution (SHADE) algorithm is capable of detecting and determining the variations of parameters in uncertain fractional-order chaotic and hyperchaotic systems, and also is supposed to be a successful and potentially promising method for handling the online identification problems with high efficiency and effectiveness.