Higher-Order ZNN Dynamics

Abstract

Several improvements of the Zhang neural network (ZNN) dynamics for solving the time-varying matrix inversion problem are presented. Introduced ZNN dynamical design is termed as ZNN models of the order p, $$p\ge 2$$, and it is based on the analogy between the proposed continuous-time dynamical systems and underlying discrete-time pth order hyperpower iterative methods for computing the constant matrix inverse. Such ZNN design is denoted by $$\hbox {ZNN}_H^p$$. Particularly, the $$\hbox {ZNN}_H^2$$ design coincides with the standard ZNN design. Moreover, $$\hbox {ZNN}_H^3$$ design represents a time-varying generalization of the previously defined ZNNCM model. In addition, an integration-enhanced noise-handling $$\hbox {ZNN}_H^p$$ model, termed as $$\hbox {IENHZNN}_H^p$$, is introduced. In the time-invariant case, we present a hybrid enhancement of the $$\hbox {ZNN}_H^p$$ model, shortly termed as $$\hbox {HZNN}_H^p$$, and investigate it theoretically and numerically. Theoretical and numerical comparisons between the improved and standard ZNN dynamics are considered.