Towards Higher-Order Zeroing Neural Network Dynamics for Solving Time-Varying Algebraic Riccati Equations

One of the most often used approaches for approximating various matrix equation problems is the hyperpower family of iterative methods with arbitrary convergence order, whereas the zeroing neural network (ZNN) is a type of neural dynamics intended for handling time-varying problems. A family of ZNN models that correlate with the hyperpower iterative methods is defined on the basis of the analogy that was discovered. These models, known as higher-order ZNN models (HOZNN), can be used to find real symmetric solutions of time-varying algebraic Riccati equations. Furthermore, a noise-handling HOZNN (NHOZNN) class of dynamical systems is introduced. The traditional ZNN and HOZNN dynamic flows are compared theoretically and numerically.