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.

Automated summary

This paper presents a new parameter estimation approach for fractional chaotic systems based on stepwise integration and response sensitivity analysis. The approach includes three parts: obtaining the numerical solution of the Grunwald-Letnikov fractional-order equations through numerical discretization, proposing a new stepwise objective function with a unique minimum value, linearizing the nonlinear objective function to reduce solving difficulty, and introducing the trust-region constraint to improve convergence performance. The efficiency and viability of the approach are demonstrated through numerical tests.