New Discretized Zeroing Neural Network Models for Solving Future System of Bounded Inequalities and Nonlinear Equations Aided With General Explicit Linear Four-Step Rule
15
Citation
31
Reference
10
Related Paper
Citation Trend
Abstract:
In this article, we derive the general explicit linear four-step (ELFS) rule with fifth-order precision systematically, together with a group of specific ELFS rules provided. Afterwards, we formulate and investigate a new and challenging discrete-time dynamic problem with relatively complex structure and future unknownness, which is simply termed future system of bounded inequalities and nonlinear equations (SBINE). With the aid of the general ELFS rule, the general ELFS-type discretized zeroing neural network (DZNN) model is proposed to solve the future SBINE. Moreover, theoretical and numerical results are presented to show the validity and high precision of the proposed general ELFS-type DZNN model. Finally, comparative numerical experiments based on a wheeled mobile robot containing several additional constraints are further performed to substantiate the applicability, validity, and superiority of the proposed general ELFS-type DZNN model.When dealing with continuous numeric features, we usually adopt feature discretization. In this work, to find the best way to conduct feature discretization, we present some theoretical analysis, in which we focus on analyzing correctness and robustness of feature discretization. Then, we propose a novel discretization method called Local Linear Encoding (LLE). Experiments on two numeric datasets show that, LLE can outperform conventional discretization method with much fewer model parameters.
Robustness
Feature (linguistics)
Cite
Citations (5)
Euler method
Mode (computer interface)
Cite
Citations (2)
In this work the discretization of the Hénon-Heiles system obtained by applying the Monaco and Normand-Cyrot method is investigated. In order to obtain dynamically valid models, several approaches covering from the choice of terms in the difference equation originated from the discretization process to the increase of the discretization order are analyzed. As a conclusion it is shown that discretized models that preserve both the symmetry and the stability of their continuous counterpart can be obtained, even for large discretization steps.
Cite
Citations (2)
Cite
Citations (2)
The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.
Collocation (remote sensing)
State variable
Temporal discretization
Orthogonal collocation
Cite
Citations (10)
Cite
Citations (9)
Discretization of continuous attributes is an important link that the rough set theory applied to the practical issues,but there is a larger choice of numerical uncertainty of the general method of discretization.In this paper,the posture difference composed by numerical difference studys the difference problem,and the results applied to the process of discretization of continuous attributes,forming a new method of discretization of continuous attributes based on the numerical difference analysis,resolving the issue of its uncertain,and finally giving a examples to verify.
Cite
Citations (0)
In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory (WENO) schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms. Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values. Extensive simulations are performed, which indicate that, the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy, and are more cost effective than WENO scheme with Runge-Kutta time discretization, while still maintaining nonoscillatory properties.
Finite difference
Shallow water equations
Runge–Kutta methods
Cite
Citations (5)
Cite
Citations (0)