On optimal solutions in a problem with two-dimensional bounded control

2018 ◽  
Author(s):  
Mariya Igorevna Ronzhina ◽  
Larisa Anatol'evna Manita
Keyword(s):  
Two Dimensional ◽  
Optimal Solutions ◽  
Bounded Control

Решения гамильтоновой системы с двумерным управлением в окрестности особой экстремали второго порядка

2021 ◽  
Vol 76 (5(461)) ◽  
pp. 201-202
Author(s):  
Мария Игоревна Ронжина ◽  
Mariya Igorevna Ronzhina ◽  
Лариса Анатольевна Манита ◽  
Larisa Anatol'evna Manita ◽  
Лев Вячеславович Локуциевский ◽  
...  
Keyword(s):  
Singular Point ◽  
Hamiltonian System ◽  
Infinite Number ◽  
Finite Time ◽  
Second Order ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Countable Number ◽  
Bounded Control ◽  
Singular Extremal

We consider a Hamiltonian system that is affine in two-dimensional bounded control that takes values in an ellipse. In the neighborhood of a singular extremal of the second order, we find two families of optimal solutions: chattering trajectories that attain the singular point in a finite time with a countable number of control switchings, and logarithmic-like spirals that reach the singular point in a finite time and undergo an infinite number of rotations.

The Nesting of Two-Dimensional Shapes Using Genetic Algorithms

1995 ◽  
Vol 209 (2) ◽  
pp. 115-124 ◽  
Author(s):  
H S Ismail ◽  
K K B Hon
Keyword(s):  
Genetic Algorithms ◽  
Evolutionary Process ◽  
Search Space ◽  
Cutting Stock ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Spatial Constraints ◽  
Global Optimal ◽  
Optimum Solution ◽  
Rapid Conversion

The general two-dimensional cutting stock problem is concerned with the optimum layout and arrangement of two-dimensional shapes within the spatial constraints imposed by the cutting stock. The main objective is to maximize the utilization of the cutting stock material. This paper presents some of the results obtained from applying a combination of genetic algorithms and heuristic approaches to the nesting of dissimilar shapes. Genetic algorithms are stochastically based optimization approaches which mimic nature's evolutionary process in finding global optimal solutions in a large search space. The paper discusses the method by which the problem is defined and represented for analysis and introduces a number of new problem-specific genetic algorithm operators that aid in the rapid conversion to an optimum solution.

A Simulated Annealing-Based Approach to Three Dimensional Component Packing

1994 ◽  
Author(s):  
Simon Szykman ◽  
Jonathan Cagan
Keyword(s):  
Simulated Annealing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Computational Approach ◽  
Vlsi Circuits ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Layout Problem ◽  
Component Layout ◽  
General Component

Abstract This paper introduces a computational approach to three dimensional component layout that employs simulated annealing to generate optimal solutions. Simulated annealing has been used extensively for two dimensional layout of VLSI circuits; this research extends techniques developed for two dimensional layout optimization to three dimensional problems which are more representative of mechanical engineering applications. In many of these applications, miniaturization trends increase the need to achieve higher packing density and fit components into smaller containers. This research addresses the three dimensional packing problem, which is a subset of the general component layout problem, as a framework in which to solve general layout problems.

Optimization of Bicycle Frames Using Genetic Algorithms

2007 ◽  
Author(s):  
Yuan Mao Huang ◽  
Kuo Juei Wang
Keyword(s):  
Genetic Algorithms ◽  
Factor Of Safety ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Dimensional Model ◽  
Equilibrium Equations ◽  
Fitness Value ◽  
Two Dimensional Model ◽  
Bicycle Frame ◽  
The Mean

A bicycle frame is optimized for the lightest weight by using genetic algorithms in this study. Stresses of five rods in the bicycle frame less than the material yielding strength with consideration of the factor of safety are the constraints. A two-dimensional model of the frame is created. Equilibrium equations are derived and loads acting on rods are determined. A known function is used to verify feasibility of the program generated. Effects of the mutation rate, the crossover rate and the number of generation on the mean and the standard deviation of the fitness value are studied. The optimal solutions with the outer diameters and the inner diameters of the front frame rods to be 0.040 m and 0.038 m, respectively, the outer diameters and the inner diameters of the rear frame rods to be 0.024 m and 0.021m, respectively, and the weight of the bicycle frame to be 0.896 kg are recommended for the bicycle frame.

Stability and constrained control for positive two-dimensional systems with delays in the second FM model

2018 ◽  
Vol 36 (2) ◽  
pp. 515-536
Author(s):  
Jian Shen ◽  
Weiqun Wang
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
Multiple Delays ◽  
Two Dimensional ◽  
Bounded Control ◽  
Delayed Systems ◽  
Closed Loop Systems ◽  
The Stability ◽  
And Control ◽  
Time Systems

Abstract This paper addresses the stability and control problem of linear positive two-dimensional discrete-time systems with multiple delays in the second Fornasini–Marchesini model. The contribution lies in three aspects. First, a novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for positive two-dimensional delayed systems. Then, a state-feedback controller is designed to ensure the non-negativity and stability of the closed-loop systems. Finally, a sufficient condition for the existence of constrained controllers is developed under the additional constraint of bounded control, which means that the control inputs and the states of the closed-loop systems are bounded. Two examples are given to validate the proposed methods.

scholarly journals On a Decomposition Method in the Problem of Operation Speed for a Linear Discrete System with Bounded Control

2019 ◽  
Vol 09 (4) ◽  
pp. 157-161
Author(s):  
D.N. Ibragimov ◽  
E.E. Turchak
Keyword(s):  
Explicit Form ◽  
Discrete System ◽  
Decomposition Theorem ◽  
Two Dimensional ◽  
State Matrix ◽  
Bounded Control ◽  
Operation Speed ◽  
Linear Discrete System ◽  
Minimum Number ◽  
Main Decomposition

The article presents the problem of operation speed for a linear discrete system with bounded control. For the case when the minimum number of steps necessary for the system to reach zero significantly exceeds the dimension of the phase space, a method of decomposition into scalar and two-dimensional subsystems is developed, based on the reduction of the state matrix to normal Jordan form. Moreover, due to the developed algorithm for adding two polyhedrons with linear complexity, it is possible to construct sets of 0-controllability for two-dimensional subsystems in an explicit form. A description of the main tools for solving the problem of operation speed is also presented, as well as the statement of the decomposition problem. Further, some properties of polyhedrons in the plane are formulated and proved, on the basis of which an algorithm for calculating the set of vertices of the sum of two polyhedrons in R2 in explicit form is developed. In conclusion, the main decomposition theorem is formulated and proved. And on the basis of the developed methods, the solution to the problem of the optimal damping speed of a high-rise structure located in the zone of seismic activity was constructed.

scholarly journals Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour

2021 ◽  
Vol 8 ◽  
Author(s):  
Tilo Strutz
Keyword(s):  
Computational Complexity ◽  
Optimization Problems ◽  
State Of The Art ◽  
Travelling Salesman Problem ◽  
Limited Time ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Major Difficulty ◽  
Travelling Salesman ◽  
New Approach

Finding the shortest tour visiting all given points at least ones belongs to the most famous optimization problems until today [travelling salesman problem (TSP)]. Optimal solutions exist for many problems up to several ten thousand points. The major difficulty in solving larger problems is the required computational complexity. This shifts the research from finding the optimum with no time limitation to approaches that find good but sub-optimal solutions in pre-defined limited time. This paper proposes a new approach for two-dimensional symmetric problems with more than a million coordinates that is able to create good initial tours within few minutes. It is based on a hierarchical clustering strategy and supports parallel processing. In addition, a method is proposed that can correct unfavorable paths with moderate computational complexity. The new approach is superior to state-of-the-art methods when applied to TSP instances with non-uniformly distributed coordinates.

scholarly journals An Improved Product Code-Based Data Hiding Scheme

2018 ◽  
Vol 8 (11) ◽  
pp. 2119
Author(s):  
Wen-Rong Zhang ◽  
Yuh-Ming Huang
Keyword(s):  
Data Hiding ◽  
The Other ◽  
Two Dimensional ◽  
Optimal Solutions ◽  
Approximation Approach ◽  
One Dimensional ◽  
Product Code ◽  
Embedding Efficiency ◽  
Matrix Embedding ◽  
Embedding Rate

This paper explores the data hiding schemes which are based on the principle of matrix embedding. Under the same embedding rate, the efficiency of each data hiding scheme is evaluated by the metric of average embedding efficiency. In the literature, both the row-column embedding and the weight approximation embedding algorithms are sub-optimal solutions for the product code-based data hiding problem. For the former, it is still based on the concept of one-dimensional (1-D) toggle syndrome, and the concept of two-dimensional (2-D) toggle syndrome is directly adopted for the latter one. Data hiding with multiple embedding channels is the practice of hiding messages into hidden media many times. Here, two multi-channel embedding-based data hiding techniques—one is the 1-D toggle syndrome-based embedding scheme (1DTS-1), and the other is the improved weight approximation-based embedding scheme (2DTS-1), are presented. In the former, the proposed one-off decision technique is used to determine the locations of the required modification bits, and the amount of modification will be reduced through utilizing the characteristics of the linear code. With the technique of the former, in the latter, the amount of modification bits can be further reduced because that a toggle array with better structure is generated, which is more suitable for being assigned as the initial toggle array while applying the weight approximation approach. The experimental results show our proposed hybrid 1-D/2-D toggle syndrome-based embedding scheme (2DTS-1) has increased the embedding efficiency by 0.1149 when compared to the weight approximation embedding algorithm. Further, the embedding efficiency of the latter one can be further and significantly enhanced through the Hamming+1 technique.

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