A Modified Quantum Bacterial Foraging Algorithm for Parameters Identification of Fractional-Order System

For many physical systems, the fractional-order system can describe the dynamics more accurately comparing with the integer-order system. However, its parameters, which include not only the identification of model coefficients but also the estimation of fractional orders, are more difficult to be identified. This paper proposes a modified quantum bacterial foraging algorithm (MQBFA) for parameters identification of the fractional-order system, and the MQBFA algorithm is a relatively new issue in recent years with strong engineering backgrounds. Not only does the proposed MQBFA algorithm apply the real number encoding of the single gene to effectively perform encoding, but it also utilizes a continuously varying rotation angle to update the rotation gate. First, a real number encoding of the single gene is designed to improve the searching efficiency of the algorithm. Second, an improved quantum rotation angle is applied to update the rotation angle continuously and adaptively. Third, the modificatory factor of probability amplitude is introduced to enrich the population diversity. In addition, to prevent the generation of invariant solutions in the early stage of quantum evolution, probability of optimal rotation angle is presented. Furthermore, the convergence of the proposed algorithm is analyzed. Based on several benchmark functions and parameters identification of the fractional-order system, simulation results and comparisons demonstrate the effectiveness of the proposed MQBFA algorithm.