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

Abstract

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.

Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

“…Therefore, the adaptation of this model to a noise-tolerant ZNN design could be the main focus of future study. To be more precise, the suggested model might be made noise-tolerant by substituting the original ZNN design with a noise-tolerant ZNN architecture, such as the one used in [37]. Moreover, future research may involve applying the proposed ZNN model to a range of other technical issues, including secure communications with application to acoustic source tracking [63] and network and power systems with application to chaotic system stabilization [64,65].…”

“…Dynamical systems for computing time-varying pseudoinverses were among their subsequent applications [34,35]. Nonlinear equation systems [36,37], linear equation systems [38,39], linear/quadratic programming [40][41][42], and generalized inversion [43,44] are among the challenges that they are currently utilized for. A ZNN model is typically constructed via two primary steps.…”

Color restoration of images through high order zeroing neural networks

“…On the other hand, recent years have seen a significant amount of research and modification done on the family of hyperpower iterations [15]. However, many HZNN models were introduced and analyzed in [16] because iterative approaches can be applied to discrete-time models and because these methods usually require beginning conditions that are approximated and sometimes may not be easily provided. A HZNN model is typically constructed through a pair of primary steps.…”

“…Furthermore, the convergence rate of the model can be modified by varying the parameter  ∈ ℝ  and the order  ≥ 2. For instance, a bigger value of  causes any HZNN model to converge even quicker [16]. It is significant to note that every HZNN model reduces to a ZNN model in the case where  = 2 since the ZNN dynamical system of (2) and the HZNN dynamical system of (4) will match.…”

Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

“…At present, the research on more challenging time-varying problems has become a new hotspot, and many new methods have been proposed and applied [1][2][3][4][5]. As a neural dynamics method with neural network background, the zeroing neural dynamics (ZND) method is proposed and applied to solve different kinds of time-varying problems [6][7][8][9][10][11][12][13][14][15][16], such as time-varying linear matrix inequality [6], robot control [9], corona virus disease diagnosis [10], matrix inversion [13,14], and timevarying nonlinear optimization [16]. Generally, the problem solving model obtained by using the ZND method is a continuous one.…”