Parameter estimation of fractional chaotic systems based on stepwise integration and response sensitivity analysis

This paper presents a new parameter estimation approach for fractional chaotic systems based on stepwise integration and response sensitivity analysis. This paper mainly consists of three parts. First, a numerical discretization scheme is introduced to obtain the numerical solution of the Grunwald-Letnikov fractional-order equations. Then, we propose a new stepwise objective function based on the single-step integration. Unlike the traditional nonlinear least-squares objective function with multiple local optimal values, the new objective function has a unique minimum value. Next, the nonlinear stepwise objective function is linearized to reduce the solving difficulty, and the trust-region constraint is introduced to raise the convergence performance of the proposed approach. Lastly, the efficiency and viability of the stepwise response sensitivity approach are demonstrated by several numerical tests.