Solving SIMO Nonlinear Systems With Euler Nonlinear Filter

This brief proposes a novel perspective for solving single input and multiple output (SIMO) nonlinear systems with multi-cost function adaptive algorithm. Based on Euler polynomials, the Euler filter with finite memory is proposed to construct a filter bank, which realizes the accurate identification of high-dimensional nonlinear systems. To improve the algorithm performance, a multi-cost function is proposed. Moreover, the mean-square stability and steady-state performance of the proposed method are rigorously analyzed. The typical FitzHugh-Nagumo (FHN) system, which fiercely exhibits chaotic dynamics, is considered for justifying the performance of this new algorithm. Numerical results highlight the solution accuracy via comparison with existing approaches.