scholarly journals An Algorithm for Solving a Class of Multiplayer Feedback-Nash Differential Games

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Jorge Herrera de la Cruz ◽  
Benjamin Ivorra ◽  
Ángel M. Ramos
Keyword(s):  
Differential Games ◽  
Numerical Algorithm ◽  
Nash Equilibria ◽  
Numerical Solutions ◽  
Iteration Step ◽  
Benchmark Problems ◽  
Value Iteration ◽  
Game Equilibrium ◽  
Computationally Expensive ◽  
Nash Differential Games

In this work, we introduce a novel numerical algorithm, called RaBVItG (Radial Basis Value Iteration Game) to approximate feedback-Nash equilibria for deterministic differential games. More precisely, RaBVItG is an algorithm based on value iteration schemes in a meshfree context. It is used to approximate optimal feedback Nash policies for multiplayer, trying to tackle the dimensionality that involves, in general, this type of problems. Moreover, RaBVItG also implements a game iteration structure that computes the game equilibrium at every value iteration step, in order to increase the accuracy of the solutions. Finally, with the purpose of validating our method, we apply this algorithm to a set of benchmark problems and compare the obtained results with the ones returned by another algorithm found in the literature. When comparing the numerical solutions, we observe that our algorithm is less computationally expensive and, in general, reports lower errors.

scholarly journals Shamanskii Method for Solving Parameterized Fuzzy Nonlinear Equations

2020 ◽  
Vol 11 (1) ◽  
pp. 24-29
Author(s):  
Sulaiman Mohammed Ibrahim ◽  
Mustafa Mamat ◽  
Puspa Liza Ghazali
Keyword(s):  
Numerical Methods ◽  
Nonlinear Equations ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Iteration Process ◽  
Benchmark Problems ◽  
Fuzzy Variables ◽  
Computationally Expensive ◽  
And Storage ◽  
Approximate Jacobian

One of the most significant problems in fuzzy set theory is solving fuzzy nonlinear equations. Numerous researches have been done on numerical methods for solving these problems, but numerical investigation indicates that most of the methods are computationally expensive due to computing and storage of Jacobian or approximate Jacobian at every iteration. This paper presents the Shamanskii algorithm, a variant of Newton method for solving nonlinear equation with fuzzy variables. The algorithm begins with Newton’s step at first iteration, followed by several Chord steps thereby reducing the high cost of Jacobian or approximate Jacobian evaluation during the iteration process. The fuzzy coe?cients of the nonlinear systems are parameterized before applying the proposed algorithm to obtain their solutions. Preliminary results of some benchmark problems and comparisons with existing methods show that the proposed method is promising.

scholarly journals Classifying streaming data using grammar-based immune programming

2021 ◽  
Author(s):  
Jaspreet Kaur Bassan
Keyword(s):  
Active Learning ◽  
Artificial Immune System ◽  
Streaming Data ◽  
Benchmark Problems ◽  
Artificial Immune ◽  
Training Process ◽  
Real World Data ◽  
Learning Technique ◽  
Computationally Expensive ◽  
Immune Programming

This work proposes a technique for classifying unlabelled streaming data using grammar-based immune programming, a hybrid meta-heuristic where the space of grammar generated solutions is searched by an artificial immune system inspired algorithm. Data is labelled using an active learning technique and is buffered until the system trains adequately on the labelled data. The system is employed in static and in streaming data environments, and is tested and evaluated using synthetic and real-world data. The performances of the system employed in different data settings are compared with each other and with two benchmark problems. The proposed classification system adapted well to the changing nature of streaming data and the active learning technique made the process less computationally expensive by retaining only those instances which favoured the training process.

scholarly journals A Numerical Algorithm for the Solutions of ABC Singular Lane–Emden Type Models Arising in Astrophysics Using Reproducing Kernel Discretization Method

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 923 ◽  
Author(s):  
Omar Abu Arqub ◽  
Mohamed S. Osman ◽  
Abdel-Haleem Abdel-Aty ◽  
Abdel-Baset A. Mohamed ◽  
Shaher Momani
Keyword(s):  
Convergence Analysis ◽  
Fractional Order ◽  
Numerical Algorithm ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Discretization Method ◽  
Fractional Models ◽  
Discretization Technique ◽  
And Mathematics

This paper deals with the numerical solutions and convergence analysis for general singular Lane–Emden type models of fractional order, with appropriate constraint initial conditions. A modified reproducing kernel discretization technique is used for dealing with the fractional Atangana–Baleanu–Caputo operator. In this tendency, novel operational algorithms are built and discussed for covering such singular models in spite of the operator optimality used. Several numerical applications using the well-known fractional Lane–Emden type models are examined, to expound the feasibility and suitability of the approach. From a numerical viewpoint, the obtained results indicate that the method is intelligent and has several features stability for dealing with many fractional models emerging in physics and mathematics, using the new presented derivative.

Sampled-Data Nash Equilibria in Differential Games with Impulse Controls

2021 ◽  
Vol 190 (3) ◽  
pp. 999-1022
Author(s):  
Utsav Sadana ◽  
Puduru Viswanadha Reddy ◽  
Tamer Başar ◽  
Georges Zaccour
Keyword(s):  
Differential Games ◽  
Nash Equilibria ◽  
Sampled Data ◽  
Impulse Controls

Introduction to the IWA Task Group on Biofilm Modeling

2004 ◽  
Vol 49 (11-12) ◽  
pp. 131-136 ◽  
Author(s):  
D.R. Noguera ◽  
E. Morgenroth
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Task Group ◽  
Benchmark Problems ◽  
Total Biomass ◽  
Advantages And Disadvantages ◽  
Biofilm Modeling ◽  
Water Association ◽  
Mixed Reactor ◽  
Detailed Presentation

An International Water Association (IWA) Task Group on Biofilm Modeling was created with the purpose of comparatively evaluating different biofilm modeling approaches. The task group developed three benchmark problems for this comparison, and used a diversity of modeling techniques that included analytical, pseudo-analytical, and numerical solutions to the biofilm problems. Models in one, two, and three dimensional domains were also compared. The first benchmark problem (BM1) described a monospecies biofilm growing in a completely mixed reactor environment and had the purpose of comparing the ability of the models to predict substrate fluxes and concentrations for a biofilm system of fixed total biomass and fixed biomass density. The second problem (BM2) represented a situation in which substrate mass transport by convection was influenced by the hydrodynamic conditions of the liquid in contact with the biofilm. The third problem (BM3) was designed to compare the ability of the models to simulate multispecies and multisubstrate biofilms. These three benchmark problems allowed identification of the specific advantages and disadvantages of each modeling approach. A detailed presentation of the comparative analyses for each problem is provided elsewhere in these proceedings.

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