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Many variations of the algebraic Riccati equation (ARE) have been used to study nonlinear system stability in the control domain in great detail. Taking the quaternion nonsymmetric ARE (QNARE) as a generalized version of ARE, the time-varying QNARE (TQNARE) is introduced. This brings us to the main objective of this work: finding the TQNARE solution. The zeroing neural network (ZNN) technique, which has demonstrated a high degree of effectiveness in handling time-varying problems, is used to do this. Specifically, the TQNARE can be solved using the high order ZNN (HZNN) design, which is a member of the family of ZNN models that correlate to hyperpower iterative techniques. As a result, a novel HZNN model, called HZ-QNARE, is presented for solving the TQNARE. The model functions fairly well, as demonstrated by two simulation tests. Additionally, the results demonstrated that, while both approaches function remarkably well, the HZNN architecture works better than the ZNN architecture. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Undoubtedly, one of the most common machine learning challenges is multiclass classification. In light of this, a novel bio-inspired neural network (NN) has been developed to address multiclass classification-related issues. Given that weights and structure determination (WASD) NNs have been acknowledged to alleviate the disadvantages of conventional back-propagation NNs, such as slow training pace and trapping in a local minimum, we developed a bio-inspired WASD algorithm for multiclass classification problems (BWASDC) by using the metaheuristic beetle antennae search (BAS) algorithm to enhance the WASD algorithm's learning process. The BWASDC's effectiveness is then evaluated through applications in occupational classification systems. It is important to mention that systems of occupational classification serve as a fundamental indicator of occupational exposure. For this reason, they are highly significant in social science research. According to the findings of four occupational classification experiments, the BWASDC model outperformed some of the most modern classification models obtainable through MATLAB's classification learner app on all fronts. [ABSTRACT FROM AUTHOR]

Dynamic Sylvester equation (DSE) problems have drawn a lot of interest from academics due to its importance in science and engineering. Due to this, the quest for the quaternion DSE (QDSE) solution is the subject of this work. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. Keeping in mind that the original ZNN can handle QDSE successfully in a noise-free environment, but it might not work in a noisy one, and the noise-resilient ZNN (NZNN) technique is also utilized. In light of that, one new ZNN model is introduced to solve the QDSE problem and one new NZNN model is introduced to solve the QDSE problem under different types of noises. Two simulation experiments and one application to control of the sine function memristor (SFM) chaotic system show that the models function superbly. [ABSTRACT FROM AUTHOR]

Due to its significance in science and engineering, time-varying linear matrix equation (LME) problems have received a lot of attention from scholars. It is for this reason that the issue of finding the minimum-norm least-squares solution of the time-varying quaternion LME (ML-TQ-LME) is addressed in this study. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. In light of that, two new ZNN models are introduced to solve the ML-TQ-LME problem for time-varying quaternion matrices of arbitrary dimension. Two simulation experiments and two practical acoustic source tracking applications show that the models function superbly. [ABSTRACT FROM AUTHOR]