Simulink Modeling and Comparison of Zhang Neural Networks and Gradient Neural Networks for Time-Varying Lyapunov Equation Solving

Abstract

In view of the great potential in parallel processing and ready implementation via hardware, neural networks are now often employed to solve online matrix algebraic problems. Recently, a special kind of recurrent neural network has been proposed by Zhang et al, which could be generalized to solving online Lyapunov equation with time-varying coefficient matrices. In comparison with gradient-based neural networks (GNN), the resultant Zhang neural networks (ZNN) perform much better on solving these timevarying problems. This paper investigates the MATLAB Simulink modeling, simulative verification and comparison of ZNN and GNN models for time-varying Lyapunov equation solving. Computer-simulation results verify that superior convergence and efficacy could be achieved by such ZNN models when solving the time-varying Lyapunov matrix equation, as compared to the GNN models.

A Reduced-Order RNN Model for Solving Lyapunov Equation Based on Efficient Vectorization Method

“…It is undeniable that the results of software simulation are consistent with those of hardware implementation. Therefore, the theoretical derivation and simulation results of the RNN in this article and in the literature (Zhang et al, 2008;Yi et al, 2011;Yi et al, 2013;Xiao and Liao, 2016;Xiao et al, 2019) can be extended to the scenarios of hardware implementation.…”

“…The simulation examples in this article are all completed on the MATLAB 2013b platform. In this article, the ode45 function of MATLAB is used to simulate the iterative process of RNN (Zhang et al, 2008). The corresponding computing performance is tested on a personal computer with Intel Core i7-4790 CPU @3.2GHz and 8 GB RAM.…”

“…Recently, due to its parallelism and convenience of hardware implementation, recurrent neural networks have been proposed and designed to solve the Lyapunov equation (Zhang et al, 2008;Yi et al, 2011;Yi et al, 2013;Xiao et al, 2019). The RNN mainly includes the Zhang neural network (ZNN) and gradient neural network (GNN) (Zhang et al, 2008). Most of the research studies on RNN focus on the improvement of model convergence.…”

“…However, as the relevant research of the RNN for solving the Lyapunov equation is still in the stage of theoretical exploration and improvement, there are no reports about hardware products of the RNN solver of the Lyapunov equation. Relevant studies (Zhang et al, 2008;Yi et al, 2011;Yi et al, 2013;Xiao and Liao, 2016;Xiao et al, 2019) simulate the execution process of the RNN hardware circuit through the form of software simulation, and this study also adopts this form. It is undeniable that the results of software simulation are consistent with those of hardware implementation.…”

A robust zeroing neural network for solving dynamic nonlinear equations and its application to kinematic control of mobile manipulator

“…AF is closely related to the effectiveness and robustness of the ZNN model, and any monotonically increasing odd AF could be considered as AF for the ZNN model [55,56]. The commonly used AFs for the ZNN model are listed in the following Table 1.…”