On the stability and convergence properties of the fuzzy learning algorithm for robotic manipulators

2002 ◽  
Author(s):  
R.A. Graca ◽  
E.Y.L. Gu
Keyword(s):  
Learning Algorithm ◽  
Robotic Manipulators ◽  
Stability And Convergence ◽  
Convergence Properties ◽  
The Stability ◽  
Fuzzy Learning

scholarly journals A New L-Stable Third Derivative Hybrid Method for Solving First Order Ordinary Differential Equations

2021 ◽  
pp. 58-69
Author(s):  
Lawrence Osa Adoghe
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Multistep Method ◽  
Stability And Convergence ◽  
Stiff Systems ◽  
Convergence Properties ◽  
Main Method ◽  
The Stability ◽  
Third Derivative

In this paper, an L-stable third derivative multistep method has been proposed for the solution of stiff systems of ordinary differential equations. The continuous hybrid method is derived using interpolation and collocation techniques of power series as the basis function for the approximate solution. The method consists of the main method and an additional method which are combined to form a block matrix and implemented simultaneously. The stability and convergence properties of the block were investigated and discussed. Numerical examples to show the efficiency and accuracy of the new method were presented.

scholarly journals Lyapunov Stability Analysis of Gradient Descent-Learning Algorithm in Network Training

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Ahmad Banakar
Keyword(s):  
Lyapunov Stability ◽  
Gradient Descent ◽  
Learning Algorithm ◽  
Stability Theorem ◽  
Stability And Convergence ◽  
Lyapunov Stability Theorem ◽  
Network Training ◽  
Learning Rates ◽  
Lyapunov Stability Analysis ◽  
The Stability

The Lyapunov stability theorem is applied to guarantee the convergence and stability of the learning algorithm for several networks. Gradient descent learning algorithm and its developed algorithms are one of the most useful learning algorithms in developing the networks. To guarantee the stability and convergence of the learning process, the upper bound of the learning rates should be investigated. Here, the Lyapunov stability theorem was developed and applied to several networks in order to guaranty the stability of the learning algorithm.

scholarly journals Formation Control of Robotic Swarm Using Bounded Artificial Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Long Qin ◽  
Yabing Zha ◽  
Quanjun Yin ◽  
Yong Peng
Keyword(s):  
Formation Control ◽  
Control Algorithm ◽  
Stability And Convergence ◽  
Multirobot Systems ◽  
Convergence Properties ◽  
Swarm Behavior ◽  
Detailed Simulation ◽  
Robotic Swarm ◽  
The Stability ◽  
Significant Attention

Formation control of multirobot systems has drawn significant attention in the recent years. This paper presents a potential field control algorithm, navigating a swarm of robots into a predefined 2D shape while avoiding intermember collisions. The algorithm applies in both stationary and moving targets formation. We define the bounded artificial forces in the form of exponential functions, so that the behavior of the swarm drove by the forces can be adjusted via selecting proper control parameters. The theoretical analysis of the swarm behavior proves the stability and convergence properties of the algorithm. We further make certain modifications upon the forces to improve the robustness of the swarm behavior in the presence of realistic implementation considerations. The considerations include obstacle avoidance, local minima, and deformation of the shape. Finally, detailed simulation results validate the efficiency of the proposed algorithm, and the direction of possible futrue work is discussed in the conclusions.

scholarly journals Stability and Convergence of Solutions to Volterra Integral Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Eleonora Messina ◽  
Antonia Vecchio
Keyword(s):  
Integral Equations ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Volterra Integral Equations ◽  
Stability And Convergence ◽  
Time Behavior ◽  
Convergence Properties ◽  
Convergence Of Solutions ◽  
Long Time ◽  
The Stability

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

Learning Control of Robot Manipulators

1993 ◽  
Vol 115 (2B) ◽  
pp. 402-411 ◽  
Author(s):  
Roberto Horowitz
Keyword(s):  
Adaptive Learning ◽  
Robot Manipulators ◽  
Learning Control ◽  
Integral Transforms ◽  
Stability And Convergence ◽  
Control Algorithms ◽  
Convergence Properties ◽  
Motor Dexterity ◽  
The Stability ◽  
Learning Schemes

Learning control encompasses a class of control algorithms for programmable machines such as robots which attain, through an iterative process, the motor dexterity that enables the machine to execute complex tasks. In this paper we discuss the use of function identification and adaptive control algorithms in learning controllers for robot manipulators. In particular, we discuss the similarities and differences between betterment learning schemes, repetitive controllers and adaptive learning schemes based on integral transforms. The stability and convergence properties of adaptive learning algorithms based on integral transforms are highlighted and experimental results illustrating some of these properties are presented.

scholarly journals Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
E. H. van Brummelen
Keyword(s):  
Incompressible Flows ◽  
Fluid Structure Interaction ◽  
Added Mass ◽  
Stability And Convergence ◽  
Time Interval ◽  
Convergence Properties ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Mass Effects ◽  
The Stability

The subiteration method, which forms the basic iterative procedure for solving fluid-structure-interaction problems, is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. In fluid-structure interaction, on short time scales the fluid appears as an added mass to the structural operator, and the stability and convergence properties of the subiteration process depend significantly on the ratio of this apparent added mass to the actual structural mass. In the present paper, we establish that the added-mass effects corresponding to compressible and incompressible flows are fundamentally different. For a model problem, we show that on increasingly small time intervals, the added mass of a compressible flow is proportional to the length of the time interval, whereas the added mass of an incompressible flow approaches a constant. We then consider the implications of this difference in proportionality for the stability and convergence properties of the subiteration process, and for the stability and accuracy of loosely coupled staggered time-integration methods.

Scalable Approach to High Coverages on Oxides via Iterative Training of a Machine-Learning Algorithm

2019 ◽  
Author(s):  
Andrew Medford ◽  
Shengchun Yang ◽  
Fuzhu Liu
Keyword(s):  
Machine Learning ◽  
Chemical Potential ◽  
Learning Algorithm ◽  
Absolute Error ◽  
Low Energy ◽  
Training Data ◽  
High Coverage ◽  
Metal Compounds ◽  
Adsorption Energies ◽  
The Stability

Understanding the interaction of multiple types of adsorbate molecules on solid surfaces is crucial to establishing the stability of catalysts under various chemical environments. Computational studies on the high coverage and mixed coverages of reaction intermediates are still challenging, especially for transition-metal compounds. In this work, we present a framework to predict differential adsorption energies and identify low-energy structures under high- and mixed-adsorbate coverages on oxide materials. The approach uses Gaussian process machine-learning models with quantified uncertainty in conjunction with an iterative training algorithm to actively identify the training set. The framework is demonstrated for the mixed adsorption of CH<sub>x</sub>, NH<sub>x</sub> and OH<sub>x</sub> species on the oxygen vacancy and pristine rutile TiO<sub>2</sub>(110) surface sites. The results indicate that the proposed algorithm is highly efficient at identifying the most valuable training data, and is able to predict differential adsorption energies with a mean absolute error of ~0.3 eV based on <25% of the total DFT data. The algorithm is also used to identify 76% of the low-energy structures based on <30% of the total DFT data, enabling construction of surface phase diagrams that account for high and mixed coverage as a function of the chemical potential of C, H, O, and N. Furthermore, the computational scaling indicates the algorithm scales nearly linearly (N<sup>1.12</sup>) as the number of adsorbates increases. This framework can be directly extended to metals, metal oxides, and other materials, providing a practical route toward the investigation of the behavior of catalysts under high-coverage conditions.

scholarly journals Numerical simulation of periodic MHD casson nanofluid flow through porous stretching sheet

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Abdullah Al-Mamun ◽  
S. M. Arifuzzaman ◽  
Sk. Reza-E-Rabbi ◽  
Umme Sara Alam ◽  
Saiful Islam ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Lewis Number ◽  
Stability And Convergence ◽  
Radiation Absorption ◽  
Physical Parameters ◽  
Theoretical Idea ◽  
Prostate Cancer Therapy ◽  
Flow Through ◽  
Explicit Finite Difference ◽  
The Stability

AbstractThe perspective of this paper is to characterize a Casson type of Non-Newtonian fluid flow through heat as well as mass conduction towards a stretching surface with thermophoresis and radiation absorption impacts in association with periodic hydromagnetic effect. Here heat absorption is also integrated with the heat absorbing parameter. A time dependent fundamental set of equations, i.e. momentum, energy and concentration have been established to discuss the fluid flow system. Explicit finite difference technique is occupied here by executing a procedure in Compaq Visual Fortran 6.6a to elucidate the mathematical model of liquid flow. The stability and convergence inspection has been accomplished. It has observed that the present work converged at, Pr ≥ 0.447 indicates the value of Prandtl number and Le ≥ 0.163 indicates the value of Lewis number. Impact of useful physical parameters has been illustrated graphically on various flow fields. It has inspected that the periodic magnetic field has helped to increase the interaction of the nanoparticles in the velocity field significantly. The field has been depicted in a vibrating form which is also done newly in this work. Subsequently, the Lorentz force has also represented a great impact in the updated visualization (streamlines and isotherms) of the flow field. The respective fields appeared with more wave for the larger values of magnetic parameter. These results help to visualize a theoretical idea of the effect of modern electromagnetic induction use in industry instead of traditional energy sources. Moreover, it has a great application in lung and prostate cancer therapy.

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