5 research outputs found
Design and Comprehensive Analysis of a Noise-Tolerant ZNN Model With Limited-Time Convergence for Time-Dependent Nonlinear Minimization
Zeroing neural network (ZNN) is a powerful tool to address the mathematical and optimization problems broadly arisen in the science and engineering areas. The convergence and robustness are always co-pursued in ZNN. However, there exists no related work on the ZNN for time-dependent nonlinear minimization that achieves simultaneously limited-time convergence and inherently noise suppression. In this article, for the purpose of satisfying such two requirements, a limited-time robust neural network (LTRNN) is devised and presented to solve time-dependent nonlinear minimization under various external disturbances. Different from the previous ZNN model for this problem either with limited-time convergence or with noise suppression, the proposed LTRNN model simultaneously possesses such two characteristics. Besides, rigorous theoretical analyses are given to prove the superior performance of the LTRNN model when adopted to solve time-dependent nonlinear minimization under external disturbances. Comparative results also substantiate the effectiveness and advantages of LTRNN via solving a time-dependent nonlinear minimization problem
Recurrent neural networks for solving matrix algebra problems
The aim of this dissertation is the application of recurrent neural
networks (RNNs) to solving some problems from a matrix algebra
with particular reference to the computations of the generalized
inverses as well as solving the matrix equations of constant (timeinvariant)
matrices. We examine the ability to exploit the correlation
between the dynamic state equations of recurrent neural networks for
computing generalized inverses and integral representations of these
generalized inverses. Recurrent neural networks are composed of
independent parts (sub-networks). These sub-networks can work
simultaneously, so parallel and distributed processing can be
accomplished. In this way, the computational advantages over the
existing sequential algorithms can be attained in real-time
applications. We investigate and exploit an analogy between the
scaled hyperpower family (SHPI family) of iterative methods for
computing the matrix inverse and the discretization of Zhang Neural
Network (ZNN) models. A class of ZNN models corresponding to the
family of hyperpower iterative methods for computing the generalized
inverses on the basis of the discovered analogy is defined. The Matlab
Simulink implementation of the introduced ZNN models is described
in the case of scaled hyperpower methods of the order 2 and 3. We
present the Matlab Simulink model of a hybrid recursive neural
implicit dynamics and give a simulation and comparison to the
existing Zhang dynamics for real-time matrix inversion. Simulation
results confirm a superior convergence of the hybrid model compared
to Zhang model
Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation
Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, zeroing neural networks (ZNNs) have been established to find the accurate solution of time-dependent Lyapunov equation (TDLE) in the noise-free conditions. However, noises are inevitable in the actual implementation process. In order to suppress the interference of various noises in practical applications, in this paper, a complex noise-resistant ZNN (CNRZNN) model is proposed and employed for the CTDLE solution. Additionally, the convergence and robustness of the CNRZNN model are analyzed and proved theoretically. For verification and comparison, three experiments and the existing noise-tolerant ZNN (NTZNN) model are introduced to investigate the effectiveness, convergence and robustness of the CNRZNN model. Compared with the NTZNN model, the CNRZNN model has more generality and stronger robustness. Specifically, the NTZNN model is a special form of the CNRZNN model, and the residual error of CNRZNN can converge rapidly and stably to order 10−5 when solving CTDLE under complex linear noises, which is much lower than order 10−1 of the NTZNN model. Analogously, under complex quadratic noises, the residual error of the CNRZNN model can converge to 2∥A∥F/ζ3 quickly and stably, while the residual error of the NTZNN model is divergent
A novel quaternion linear matrix equation solver through zeroing neural networks with applications to acoustic source tracking
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
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum