scholarly journals CONSTRUCTION OF MINIMAX CONTROL FOR ALMOST CONSERVATIVE CONTROLLED DYNAMIC SYSTEMS WITH THE LIMITED PERTURBATIONS

2017 ◽  
Vol 2 ◽  
pp. 9-15
Author(s):  
Iryna Svyatovets
Keyword(s):  
Riccati Equation ◽  
Infinite System ◽  
Conservative System ◽  
Coefficient Matrix ◽  
Necessary Condition ◽  
Existence Of A Solution ◽  
Minimax Control ◽  
System Of Matrix Equations ◽  
System A ◽  
The Matrix

The problem is considered for constructing a minimax control for a linear stationary controlled dynamical almost conservative system (a conservative system with a weakly perturbed coefficient matrix) on which an unknown perturbation with bounded energy acts. To find the solution of the Riccati equation, an approach is proposed according to which the matrix-solution is represented as a series expansion in a small parameter and the unknown components of this matrix are determined from an infinite system of matrix equations. A necessary condition for the existence of a solution of the Riccati equation is formulated, as well as theorems on additive operations on definite parametric matrices. A condition is derived for estimating the parameter appearing in the Riccati equation. An example of a solution of the minimax control problem for a gyroscopic system is given. The system of differential equations, which describes the motion of a rotor rotating at a constant angular velocity, is chosen as the basis.

scholarly journals Solusi Sistem Persamaan Linear Fuzzy

Matematika ◽  
2017 ◽  
Vol 16 (2) ◽  
Author(s):  
I. Irmawati ◽  
Icih Sukarsih ◽  
R. Respitawulan
Keyword(s):  
Fuzzy Numbers ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Real Coefficient ◽  
Necessary And Sufficient Condition ◽  
Unknown Variable ◽  
Fuzzy Variables ◽  
System A ◽  
The Matrix ◽  
Necessary And Sufficient

Abstract. Let A with A is n x n real coefficient matrix which is real numbers,  is vector of n unknown fuzzy variables, and   is  n fuzzy  constants vector. This system is named fuzzy linear equations system. To find  the solution of fuzzy linear equations system A , this system must be transformed into  with B is   2n x 2n coefficient matrix,  is 2n x 1 matrix of unknown variable , and  is 2n x 1 matrix of constants. The solution of   indirectly is the solution of A  because the matrix  corresponded to  is not necessarily fuzzy numbers. The necessary and sufficient condition to make the matrix  become the solution of A   is must be non negative. To help finding the solution  fuzzy linear equations system, on algorithm is built and implemented on Matlab.Keywords: Fuzzy Linear Equations System, Fuzzy  Numbers, Algorithm. Abstrak. Diberikan  A  dengan A adalah matriks koefisien berukuran n x n yang merupakan bilangan real,  adalah n variabel fuzzy yang tidak diketahui,  adalah vektor konstanta fuzzy dengan panjang n. Sistem tersebut dinamakan sistem persamaan linear fuzzy. Dalam mencari solusi sistem persamaan linear fuzzy A sistem tersebut harus ditransformasikan dalam bentuk  dengan B adalah matriks koefisien berukuran 2n x 2n, adalah matriks 2n x 1 dari variabel yang tidak diketahui, dan adalah matriks 2n x 1 dari konstanta. Solusi dari  tidak langsung menjadi solusi A , karena  yang bersesuaian dengan belum tentu berupa bilangan fuzzy. Syarat perlu dan cukup agar  merupakan solusi A  yaitu  harus non negatif. Untuk memudahkan mencari solusi dari sistem persamaan linear fuzzy perlu dibangun algoritma solusi sistem persamaan linear fuzzy dan implementasinya menggunakan Matlab.Kata Kunci : Sistem Persamaan Linear Fuzzy, Bilangan Fuzzy, Algoritma.

scholarly journals The Meaning of the Matrix: Towards a Cybernetic Critical Theory of Capitalism

2018 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Shay Hershkovitz
Keyword(s):  
Social Systems ◽  
Theoretical Concept ◽  
Social Actors ◽  
System A ◽  
The Social ◽  
Social Entity ◽  
Key Concepts ◽  
The Matrix ◽  
Critical Approaches ◽  
Operational Logic

Marxist criticism is most discernible; despite the oft-repeated claim that it is now irrelevant, belonging to an age now past. This essay assumes that criticism originating in the Marxist school of thought continue to be relevant also in this present time; though it may need to be further developed and improved by integrating newer critical approaches into the classic Marxist discourse. This essay therefore integrates basic Marxist ideas with key concepts from ‘social systems theory’; especially the theory of the German sociologist Niklas Luhmann's. In this light, capitalism is conceptualized here as a ‘super (social) system’: a meaning-creating social entity, in which social actors, behaviors and structures are realized. This theoretical concept and terminology emphasizes the social construction of control and stability, when discussing the operational logic of capitalism.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

scholarly journals Generalized Euclidean Least Square Approximation

2018 ◽  
pp. 1-10
Author(s):  
A. S. Oke ◽  
S. M. Akintewe ◽  
A. G. Akinbande
Keyword(s):  
Exponential Function ◽  
Existence And Uniqueness ◽  
Coefficient Matrix ◽  
Least Square ◽  
Data Set ◽  
Condensation Method ◽  
The Matrix

A Generalised Euclidean Least Square Approximation (ELS) is derived in this paper. The Generalised Euclidean Least Square Approximation is derived by generalizing the interpolation of n arbitrary data set to approximate functions. Existence and uniqueness of the ELS schemes are shown by establishing the invertibility of the coefficient matrix using condensation method to reduce the matrix. The method is illustrated for exponential function and the results are compared to the classical Maclaurin’s series.

scholarly journals THE GENERALIZED MATRIX VALUED HYPERGEOMETRIC EQUATION

2010 ◽  
Vol 21 (02) ◽  
pp. 145-155 ◽  
Author(s):  
P. ROMÁN ◽  
S. SIMONDI
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Hypergeometric Functions ◽  
Spherical Functions ◽  
Hypergeometric Equation ◽  
Necessary Condition ◽  
Hypergeometric Differential Equation ◽  
The Matrix ◽  
Generalized Matrix

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in [4]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in [4] to identify the corresponding matrix hypergeometric functions nFm. We prove that, if n = m + 1, these functions are analytic for |z| < 1 and we give a necessary condition for the convergence on the unit circle |z| = 1.

scholarly journals D-Optimal Slope Design for Second Degree Kronecker Model Mixture Experiment With Three Ingredients

2020 ◽  
Vol 9 (2) ◽  
pp. 30
Author(s):  
Ngigi Peter Kung’u ◽  
J. K. Arap Koske ◽  
Josphat K. Kinyanjui
Keyword(s):  
Information Matrix ◽  
Coefficient Matrix ◽  
Three Dimensions ◽  
Matrix Means ◽  
The Matrix ◽  
Optimal Values ◽  
The Moment ◽  
Product Algebra ◽  
Slope Design ◽  
Second Degree

This study presents an investigation of an optimal slope design in the second degree Kronecker model for mixture experiments in three dimensions. The study is restricted to weighted centroid designs, with the second degree Kronecker model. A well-defined coefficient matrix is used to select a maximal parameter subsystem for the model since its full parameter space is inestimable. The information matrix of the design is obtained using a linear function of the moment matrices for the centroids and directly linked to the slope matrix. The discussion is based on Kronecker product algebra which clearly reflects the symmetries of the simplex experimental region. Eventually the matrix means are used in determining optimal values of the efficient developed design.

Leontev Input-Output Balance Model as a Dynamic System Control Problem

2021 ◽  
pp. 66-82
Author(s):  
S.N. Masaev
Keyword(s):  
Dynamic System ◽  
Matrix Representation ◽  
External Environment ◽  
Balance Model ◽  
System Control ◽  
Operational Mode ◽  
Input Output ◽  
System A ◽  
The Matrix ◽  
Research Show

The purpose of the study was to determine the problem of control of a dynamic system of higher dimension. Relying on Leontev input-output balance, we formalized the dynamic system and synthesized its control. Within the research, we developed a mathematical model that combines different working objects that consume and release various resources. The value of the penalty for all nodes and objects is introduced into the matrix representation of the problem, taking into account various options for their interaction, i.e., the observation problem. A matrix representation of the planning task at each working object is formed. For the formed system, a control loop is created; the influencing parameters of the external environment are indicated. We calculated the system operational mode, taking into account the interaction of the nodes of objects with each other when the parameters of the external environment influence them. Findings of research show that in achieving a complex result, the system is inefficient without optimal planning and accounting for the matrix of penalties for the interaction of nodes and objects of the dynamic system with each other. In a specific example, for a dynamic system with a dimension of 4.8 million parameters, we estimated the control taking into account the penalty matrix, which made it possible to increase the inflow of additional resources from the outside by 2.4 times from 130 billion conv. units up to 310 conv. units in 5 years. Taking into account the maximum optimization of control in the nodes, an increase of 3.66 times in the inflow of additional resources was ensured --- from 200.46 to 726.62 billion rubles

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