A Novel Zeroing Neurodynamic Method Based on Discrete Fuzzy Control System: Design, Analysis, and Verification

Considering the extensive research on zeroing neurodynamic (ZN), a self-adaptive and enhanced fixed-time convergent ZN (SEFC-ZN) method for addressing time-variant problems is presented in this article based on a discrete fuzzy matrix (DFM) design parameter and a novel advanced sign-bi-power activation function (NASbpAf). Due to the distinctive design of the DFM design parameter and NASbpAf, the proposed SEFC-ZN method possesses prominent self-adaptivity and enhanced fixed-time convergence. Specifically, the DFM design parameter is actually a matrix with all elements generated from a discrete fuzzy control system, so it can self-adaptively adjust the convergence rate of every error in the SEFC-ZN method resulting in the self-adaptivity. This feature is greatly different from the conventional scalar design parameters whose values are usually fixed or increase indefinitely and different errors in the ZN method can only be adjusted by the same design parameter. By summarizing the characteristic of the activation functions designed previously according to the SbpAf, it is found that keeping two terms of the SbpAf and adding extra terms can improve the performance of the ZN method. Thereout, built on the SbpAf, the NASbpAf is presented which can make the SEFC-ZN method realize the enhanced fixed-time convergence. Three theoretical analyses and proofs, together with relative corollaries, conclude the properties of the SEFC-ZN method and the advantages of the DFM design parameter and NASbpAf. A numerical experiment about solving time-variant nonlinear equations by the SEFC-ZN method and an application to the linear-quadratic optimal control strongly verify the proposed theory and method.