Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems

Vasilios N. Katsikis; Predrag S. Stanimirović; Spyridon D. Mourtas; Xiao, Lin; Stanujkić, Dragiša; Karabašević, Darjan

Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems

Citation:

Katsikis, V. N., Stanimirović, P. S., Mourtas, S. D., Xiao, L., Stanujkić, D., & Karabašević, D. (2023). Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems. Neural Processing Letters. presented at the 2023. Copy at http://www.tinyurl.com/2zztcoq3

Abstract:

This paper presents a dynamic model based on neutrosophic numbers and a neutrosophic logic engine. The introduced neutrosophic logic/fuzzy adaptive Zeroing Neural Network dynamic is termed NSFZNN and represents an improvement over the traditional Zeroing Neural Network (ZNN) design. The model aims to calculate the matrix pseudo-inverse and the minimum-norm least-squares solutions of time-varying linear systems. The improvement of the proposed model emerges from the advantages of neutrosophic logic over fuzzy and intuitionistic fuzzy logic in solving complex problems associated with predictions, vagueness, uncertainty, and imprecision. We use neutrosphication, de-fuzzification, and de-neutrosophication instead of fuzzification and de-fuzzification exploited so far. The basic idea is based on the known advantages of neutrosophic systems compared to fuzzy systems. Simulation examples and engineering applications on localization problems and electrical networks are presented to test the efficiency and accuracy of the proposed dynamical system.

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National and Kapodistrian University of Athens
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Phone number: (+30) 210-3689489
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Email: vaskatsikis@econ.uoa.gr
URL: http://scholar.uoa.gr/vaskatsikis
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Recent Publications

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Numerous people are applying for bank loans as a result of the banking industry’s expansion, but because banks only have a certain amount of assets to lend to, they can only do so to a certain number of applicants. Therefore, the banking industry is very interested in finding ways to reduce the risk factor involved in choosing the safe applicant in order to save lots of bank resources. These days, machine learning greatly reduces the amount of work needed to choose the safe applicant. Taking this into account, a novel weights and structure determination (WASD) neural network has been built to meet the aforementioned two challenges of credit approval and loan approval, as well as to handle the unique characteristics of each. Motivated by the observation that WASD neural networks outperform conventional back-propagation neural networks in terms of sluggish training speed and being stuck in local minima, we created a bio-inspired WASD algorithm for binary classification problems (BWASD) for best adapting to the credit or loan approval model by utilizing the metaheuristic beetle antennae search (BAS) algorithm to improve the learning procedure of the WASD algorithm. Theoretical and experimental study demonstrate superior performance and problem adaptability. Furthermore, we provide a complete MATLAB package to support our experiments together with full implementation and extensive installation instructions.

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The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called ’ZQ-ARE’ that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor’s flight control system faster than the traditional differential-algebraic Riccati equation solution.

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Generalized inverses are extremely effective in many areas of mathematics and engineering. The zeroing neural network (ZNN) technique, which is currently recognized as the state-of-the-art approach for calculating the time-varying Moore-Penrose matrix inverse, is investigated in this study as a solution to the problem of calculating the time-varying minimum rank outer inverse (TV-MROI) with prescribed range and/or TV-MROI with prescribed kernel. As a result, four novel ZNN models are introduced for computing the TV-MROI, and their efficiency is examined. Numerical tests examine and validate the effectiveness of the introduced ZNN models for calculating TV-MROI with prescribed range and/or prescribed kernel.

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Vasilios Katsikis

Professor, Economics

Zeroing Neural Network Based on Neutrosophic Logic for Calculating Minimal-Norm Least-Squares Solutions to Time-Varying Linear Systems

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