scholarly journals Optimization of Parameters of Asymptotically Stable Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Anna Guerman ◽  
Ana Seabra ◽  
Georgi Smirnov
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Mathematical Programming ◽  
Mathematical Programming Problem ◽  
Discrete Problem ◽  
Asymptotically Stable ◽  
Stabilization System ◽  
Optimal Parameters ◽  
Optimization Of Parameters ◽  
Satellite Stabilization

This work deals with numerical methods of parameter optimization for asymptotically stable systems. We formulate a special mathematical programming problem that allows us to determine optimal parameters of a stabilizer. This problem involves solutions to a differential equation. We show how to chose the mesh in order to obtain discrete problem guaranteeing the necessary accuracy. The developed methodology is illustrated by an example concerning optimization of parameters for a satellite stabilization system.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

scholarly journals Formulating Intuitionistic Fuzzy Regression Models: A Mathematical Programming Approach

2021 ◽  
Author(s):  
Sheng-Hsing Nien ◽  
Liang-Hsuan Chen
Keyword(s):  
Mathematical Programming ◽  
Regression Models ◽  
Fuzzy Regression ◽  
Distance Measures ◽  
Programming Approach ◽  
Mathematical Programming Problem ◽  
Explanatory Variables ◽  
Intuitionistic Fuzzy ◽  
Mathematical Programming Approach ◽  
Ordinary Regression

Abstract This study develops a mathematical programming approach to establish intuitionistic fuzzy regression models (IFRMs) by considering the randomness and fuzziness of intuitionistic fuzzy observations. In contrast to existing approaches, the IFRMs are established in terms of five ordinary regression models representing the components of the estimated triangular intuitionistic fuzzy response variable. The optimal parameters of the five ordinary regression models are determined by solving the proposed mathematical programming problem, which is linearized to make the resolution process efficient. Based on the concepts of randomness and fuzziness in the formulation processes, the proposed approach can improve on existing approaches’ weaknesses with establishing IFRMs, such as the limitation of symmetrical triangular membership (or non-membership) functions, the determination of parameter signs in the model, and the wide spread of the estimated responses. In addition, some numerical explanatory variables included in the intuitionistic fuzzy observations are also allowed in the proposed approach, even though it was developed for intuitionistic fuzzy observations. In contrast to existing approaches, the proposed approach is general and flexible in applications. Comparisons show that the proposed approach outperforms existing approaches in terms of similarity and distance measures.

scholarly journals ROLE OF KUHN-TUCKER CONDITIONS IN ELASTICITY EQUATIONS IN TERMS OF STRESSES

2000 ◽  
Vol 6 (2) ◽  
pp. 104-112
Author(s):  
Ela Chraptovič ◽  
Juozas Atkočiūnas
Keyword(s):  
Mathematical Programming ◽  
System Integration ◽  
Minimum Principle ◽  
Functional Space ◽  
Elasticity Problem ◽  
Mathematical Programming Problem ◽  
Variation Principle ◽  
Three Dimension ◽  
Strain Compatibility ◽  
Elasticity Equations

Solution of the elasticity problem in terms of stresses leads to the stress vector six components, satisfying the Beltrami compatibility eqns and boundary conditions, evaluation. A direct integration of the nine differential eqns system in respect of the six stress components is difficult to realise practically. This is the reason why often the Casigliano variation principle to solve the boundary elasticity problem in terms of stresses is applied. An application of the above-mentioned principle ensures the satisfaction of all the six Saint-Venant strain compatibility eqns (see the works of Southwell, Kliushnikov, a.o.). Castigliano variation principle does not define the number of independent strain compatibility eqns. Thus, it is not clear whether the elasticity problem eqns system in terms of stresses is over-defined or not. The strain compatibility eqns for an ideal elastic body is investigated in the article by means of the mathematical programming theory. A mathematical model to evaluate the statically admissible stresses is formulated on the basis of complementary energy minimum principle. It is proved that the strain compatibility eqns mean the Kuhn-Tucker optimality conditions of the mathematical programming problem. The method to formulate the strain compatibility eqns in respect of the statically admissible stresses defining eqns formulation technique is revealed. The proposed method is illustrated to achieve the six component stresses vector in functional space for the three-dimension problem: usually the solution of the elasticity problem in terms of the stresses is realised via the nine eqns system integration. The Kuhn-Tucker conditions allowed to confirm an original but not usually applied Washizu conclusion about Cauchy geometrical compatibility eqns.

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