scholarly journals Solving systems of matrix equations of the second degree

2021 ◽  
pp. 52-56
Author(s):  
Anastasiya Nedashkovska
Keyword(s):  
Optimization Problems ◽  
Polynomial Matrix ◽  
Theoretical Calculations ◽  
System Optimization ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Real Numbers ◽  
Universal Approach ◽  
Matrix Fraction ◽  
Second Degree

Matrix equations and systems of matrix equations are widely used in control system optimization problems. However, the methods for their solving are developed only for the most popular matrix equations – Riccati and Lyapunov equations, and there is no universal approach for solving problems of this class. This paper summarizes the previously considered method of solving systems of algebraic equations over a field of real numbers [1] and proposes a scheme for systems of polynomial matrix equations of the second degree with many unknowns. A recurrent formula for fractionalization a solution into a continued matrix fraction is also given. The convergence of the proposed method is investigated. The results of numerical experiments that confirm the validity of theoretical calculations and the effectiveness of the proposed scheme are presented.

Optimum Selection of Hydraulic Devices for Water Hammer Control in the Pipeline Systems Using Genetic Algorithm

2003 ◽  
Author(s):  
Bong Seong Jung ◽  
Bryan W. Karney
Keyword(s):  
Genetic Algorithm ◽  
Steady State ◽  
Optimization Problems ◽  
System Optimization ◽  
Water Hammer ◽  
Pipeline System ◽  
Optimal Size ◽  
Protection Strategy ◽  
Hydraulic Devices ◽  
Selection Of

Genetic algorithms have been used to solve many water distribution system optimization problems, but have generally been limited to steady state or quasi-steady state optimization. However, transient events within pipe system are inevitable and the effect of water hammer should not be overlooked. The purpose of this paper is to optimize the selection, sizing and placement of hydraulic devices in a pipeline system considering its transient response. A global optimal solution using genetic algorithm suggests optimal size, location and number of hydraulic devices to cope with water hammer. This study shows that the integration of a genetic algorithm code with a transient simulator can improve both the design and the response of a pipe network. This study also shows that the selection of optimum protection strategy is an integrated problem, involving consideration of loading condition, device and system characteristics, and protection strategy. Simpler transient control systems are often found to outperform more complex ones.

scholarly journals GEKKO Optimization Suite

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 106 ◽  
Author(s):  
Logan Beal ◽  
Daniel Hill ◽  
R. Martin ◽  
John Hedengren
Keyword(s):  
Optimal Control ◽  
Optimization Problems ◽  
Object Oriented ◽  
Differential Algebraic Equations ◽  
Mixed Integer ◽  
Modeling Languages ◽  
Algebraic Equations ◽  
Simulation And Optimization ◽  
Algebraic Modeling Languages ◽  
Real Time Optimization

This paper introduces GEKKO as an optimization suite for Python. GEKKO specializes in dynamic optimization problems for mixed-integer, nonlinear, and differential algebraic equations (DAE) problems. By blending the approaches of typical algebraic modeling languages (AML) and optimal control packages, GEKKO greatly facilitates the development and application of tools such as nonlinear model predicative control (NMPC), real-time optimization (RTO), moving horizon estimation (MHE), and dynamic simulation. GEKKO is an object-oriented Python library that offers model construction, analysis tools, and visualization of simulation and optimization. In a single package, GEKKO provides model reduction, an object-oriented library for data reconciliation/model predictive control, and integrated problem construction/solution/visualization. This paper introduces the GEKKO Optimization Suite, presents GEKKO’s approach and unique place among AMLs and optimal control packages, and cites several examples of problems that are enabled by the GEKKO library.

scholarly journals Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Berna Bülbül ◽  
Mehmet Sezer
Keyword(s):  
Matrix Method ◽  
Numerical Approach ◽  
Duffing Equation ◽  
Matrix Equations ◽  
Algebraic Equations ◽  
Solution Function ◽  
Numerical Examples ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
The Matrix

We have suggested a numerical approach, which is based on an improved Taylor matrix method, for solving Duffing differential equations. The method is based on the approximation by the truncated Taylor series about center zero. Duffing equation and conditions are transformed into the matrix equations, which corresponds to a system of nonlinear algebraic equations with the unknown coefficients, via collocation points. Combining these matrix equations and then solving the system yield the unknown coefficients of the solution function. Numerical examples are included to demonstrate the validity and the applicability of the technique. The results show the efficiency and the accuracy of the present work. Also, the method can be easily applied to engineering and science problems.

scholarly journals Intelligent Total Transportation Management System for Future Smart Cities

2020 ◽  
Vol 10 (24) ◽  
pp. 8933
Author(s):  
Dinh Dung Nguyen ◽  
József Rohács ◽  
Dániel Rohács ◽  
Anita Boros
Keyword(s):  
Public Transport ◽  
Management System ◽  
Optimization Problems ◽  
Smart Cities ◽  
System Optimization ◽  
Preliminary Evaluation ◽  
Total System ◽  
Sensors And Actuators ◽  
Total Energy Consumption ◽  
Transportation Management

Smart mobility and transportation, in general, are significant elements of smart cities, which account for more than 25% of the total energy consumption related to smart cities. Smart transportation has seven essential sections: leisure, private, public, business, freight, product distribution, and special transport. From the management point of view, transportation can be classified as passive or non-cooperating, semi-active or simple cooperating, active or cooperating, contract-based, and priority transportation. This approach can be applied to public transport and even to passengers of public transport. The transportation system can be widely observed, analyzed, and managed using an extensive distribution network of sensors and actuators integrated into an Internet of Things (IoT) system. The paper briefly discusses the benefits that the IoT can offer for smart city transportation management. It deals with the use of a hierarchical approach to total transportation management, namely, defines the concept, methodology, and required sub-model developments, which describes the total system optimization problems; gives the possible system and methodology of the total transportation management; and demonstrates the required sub-model developments by examples of car-following models, formation motion, obstacle avoidances, and the total management system implementation. It also introduces a preliminary evaluation of the proposed concept relative to the existing systems.

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