scholarly journals Lyapunov matrices approach to the parametric optimization of a neutral system

2016 ◽  
Vol 26 (1) ◽  
pp. 81-93 ◽  
Author(s):  
Jozef Duda
Keyword(s):  
Initial Function ◽  
Lyapunov Functional ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Neutral System ◽  
Quadratic Performance Index ◽  
Parametric Optimization Problem ◽  
Lyapunov Matrix ◽  
Quadratic Performance ◽  
Index Of Quality

In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system. The Lyapunov functional is determined by means of the Lyapunov matrix.

scholarly journals Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays

2016 ◽  
Vol 26 (3) ◽  
pp. 367-381
Author(s):  
Jozef Duda
Keyword(s):  
Time Delay ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Delay System ◽  
Delay Systems ◽  
Quadratic Performance Index ◽  
Parametric Optimization Problem ◽  
Two Delays ◽  
Lyapunov Matrix ◽  
Quadratic Performance

AbstractIn the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with two commensurate delays and a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of the Lyapunov functional for the initial function of time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.

scholarly journals Lyapunov matrices approach to the parametric optimization of time-delay systems

2015 ◽  
Vol 25 (3) ◽  
pp. 279-288 ◽  
Author(s):  
Józef Duda
Keyword(s):  
Time Delay ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Delay System ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Quadratic Performance Index ◽  
Parametric Optimization Problem ◽  
Lyapunov Matrix ◽  
Quadratic Performance

AbstractIn the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix

scholarly journals Parametric optimization of neutral linear system with two delays with P-controller

2011 ◽  
Vol 21 (4) ◽  
pp. 363-372 ◽  
Author(s):  
Józef Duda
Keyword(s):  
Linear System ◽  
Performance Index ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Neutral Type ◽  
Neutral System ◽  
Initial State ◽  
Quadratic Performance Index ◽  
Two Delays ◽  
Quadratic Performance

Parametric optimization of neutral linear system with two delays with P-controller In the paper the problem of parametric optimization of a linear neutral system with two delays accomplished with respect to the integral quadratic performance index is formulated and solved. A method of computing the value of performance index relies on determining such a Lyapunov functional defined on the state space that its value for the initial state is equal to that of performance index. In the paper the form of Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of the theory discussed is presented. It concerns a system with the P-controller designed to control a plant with two delays both retarded and neutral type. For such a system the value of the considered performance index is determined.

scholarly journals Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Shu-qiang Shan ◽  
Yu Han ◽  
Nan-jing Huang
Keyword(s):  
Nash Equilibria ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Upper Semicontinuity ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Quasiequilibrium Problems ◽  
Parametric Variational Inequality ◽  
Parametric Optimization Problem ◽  
Vector Quasiequilibrium Problems

We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.

Parametric Optimization for Structural Design Problems

2019 ◽  
Author(s):  
Krupakaran Ravichandran ◽  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Structural Design ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Nonlinear Constraint ◽  
Computational Performance ◽  
Design Variables ◽  
Input Parameters ◽  
Parametric Optimization Problem ◽  
Objective Function Values

Abstract Parametric Optimization is used to solve problems that have certain design variables as implicit functions of some independent input parameters. The optimal solutions and optimal objective function values are provided as functions of the input parameters for the entire parameter space of interest. Since exact solutions are available merely for parametric optimization problems that are linear or convex-quadratic, general non-convex non-linear problems require approximations. In the present work, we apply three parametric optimization algorithms to solve a case study of a benchmark structural design problem. The algorithms first approximate the nonlinear constraint(s) and then solve the optimization problem. The accuracy of their results and their computational performance are then compared to identify a suitable algorithm for structural design applications. Using the identified method, sizing optimization of a truss structure for varying load conditions such as a varying load direction is considered and solved as a parametric optimization problem to evaluate the performance of the identified algorithm. The results are also compared with non-parametric optimization to assess the accuracy of the solution and computational performance of the two methods.

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