Governing Parameter Changes in Nonlinear Parameter-Dependent Optimization Problems

2013 ◽  
Author(s):  
Rohit Gupta ◽  
Ilya V. Kolmanovsky
Keyword(s):  
Hybrid Electric Vehicles ◽  
Optimization Problems ◽  
Maximum Speed ◽  
Governing Parameter ◽  
Acceptable Error ◽  
Root Finding ◽  
Flight Path Angle ◽  
Predictor Corrector ◽  
Parameter Dependent ◽  
The Given

The paper treats a class of parameter-dependent optimization/root finding problems where the minimizer or a real root need to be determined as a function of parameter. Applications of parameter-dependent optimization include spacecraft debris avoidance, adaptive control of Hybrid Electric Vehicles, engine mapping and model predictive control. In these and other problems, the parameter changes can be controlled either directly or indirectly. In this paper, the error analysis of a dynamic predictor-corrector Newton’s type algorithm is presented. Based on this analysis, an approach to govern the changes in the parameter to enable the algorithm to track the minimizer within an acceptable error bound is described. Two simulation examples are presented. In the first example the objective is to minimize the distance between points on a curve and a given set and simultaneously move as fast as possible along the given curve. In the second example we illustrate the use of this technique for aircraft flight envelope estimation. Specifically, we estimate maximum speed of an aircraft as a function of its altitude and flight path angle.

scholarly journals Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

2020 ◽  
Vol 42 (1) ◽  
pp. 65-84
Author(s):  
Jinzhong Ma ◽  
Yong Xu ◽  
Yongge Li ◽  
Ruilan Tian ◽  
Shaojuan Ma ◽  
...  
Keyword(s):  
Lévy Noise ◽  
Stable Model ◽  
Efficient Tool ◽  
Escape Probability ◽  
Critical Transitions ◽  
Current State ◽  
Undesirable State ◽  
Parameter Dependent ◽  
Levy Noise ◽  
The Given

AbstractIn real systems, the unpredictable jump changes of the random environment can induce the critical transitions (CTs) between two non-adjacent states, which are more catastrophic. Taking an asymmetric Lévy-noise-induced tri-stable model with desirable, sub-desirable, and undesirable states as a prototype class of real systems, a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out. We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability, which is named as the absorbed region. Then, a new concept of the parameter dependent basin of the unsafe regime (PDBUR) under the asymmetric Lévy noise is introduced. It is an efficient tool for approximately quantifying the ranges of the parameters, where the noise-induced CTs from the desirable state directly to the undesirable one may occur. More importantly, it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

Lassa hemorrhagic fever model using new generalized Caputo-type fractional derivative operator

2021 ◽  
pp. 2150055
Author(s):  
Pushpendra Kumar ◽  
Vedat Suat Erturk ◽  
Abdullahi Yusuf ◽  
Tukur Abdulkadir Sulaiman
Keyword(s):  
Pregnant Women ◽  
Fractional Order ◽  
Research Work ◽  
Hemorrhagic Fever ◽  
Hemorrhagic Disease ◽  
Lassa Virus ◽  
Research Fields ◽  
Negative Impacts ◽  
Predictor Corrector ◽  
The Given

In some of the previous decades, we have observed that mathematical modeling has become one of the most interesting research fields and has attracted many researchers. In this regard, thousands of researchers have proposed different varieties of mathematical models to study the dynamics of a number of real-world problems. This research work is framed to analyzing the structure of the well-known Lassa hemorrhagic epidemic; a dangerous epidemic for pregnant women, via new generalized Caputo type noninteger order derivative with the help of a modified Predictor–Corrector scheme. Lassa hemorrhagic disease is an epidemical and biocidal fever, whose negative impacts were initially recognized in the countries of Africa. This virus has killed many pregnant women as compared to the Ebola epidemic. It was noticed that Lassa virus was isolated in Vero cell cultures from a blood pattern, and after 12 days it was ejective, after the climb of the sickness. In this research study, necessary theorems and lemmas are reminded to prove the existence of a unique solution and stability of given fractional approximation scheme. All necessary results are reminded to confirm the effectiveness of the proposed approximation algorithm by graphical observations for various fractional-order values. In our practical calculations, we plotted the graphs for two different values of natural death rate along with various values of given fractional-order operator. Our major target is to show the importance of the proposed modified version of the Predictor–Corrector algorithm in epidemic studies by exploring the given Lassa hemorrhagic fever dynamics.

Opposition-based learning Multi-Verse Optimizer with disruption operator for optimization problems

2021 ◽  
Author(s):  
Mohammad Shehab ◽  
Laith Abualigah
Keyword(s):  
Real World ◽  
Optimization Problems ◽  
Second Stage ◽  
Opposition Based Learning ◽  
High Fitness ◽  
Fitness Value ◽  
Speed Up ◽  
Disruption Operator ◽  
The Given ◽  
Real World Problems

Abstract Multi-Verse Optimizer (MVO) algorithm is one of the recent metaheuristic algorithms used to solve various problems in different fields. However, MVO suffers from a lack of diversity which may trapping of local minima, and premature convergence. This paper introduces two steps of improving the basic MVO algorithm. The first step using Opposition-based learning (OBL) in MVO, called OMVO. The OBL aids to speed up the searching and improving the learning technique for selecting a better generation of candidate solutions of basic MVO. The second stage, called OMVOD, combines the disturbance operator (DO) and OMVO to improve the consistency of the chosen solution by providing a chance to solve the given problem with a high fitness value and increase diversity. To test the performance of the proposed models, fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems, and seven CEC 2011 real-world problems were used in both phases of the enhancement. The second step, known as OMVOD, incorporates the disruption operator (DO) and OMVO to improve the accuracy of the chosen solution by giving a chance to solve the given problem with a high fitness value while also increasing variety. Fifteen CEC 2015 benchmark functions problems, thirty CEC 2017 benchmark functions problems and seven CEC 2011 real-world problems were used in both phases of the upgrade to assess the accuracy of the proposed models.

scholarly journals Graph Theoretic Techniques in the Analysis of Uniquely Localizable Sensor Networks

2009 ◽  
pp. 146-173 ◽  
Author(s):  
Bill Jackson ◽  
Tibor Jordán
Keyword(s):  
Graph Theory ◽  
Sensor Networks ◽  
Optimization Problems ◽  
Partial Information ◽  
Two Dimensions ◽  
Localization Problem ◽  
Graph Theoretic ◽  
Network Localization ◽  
Exact Location ◽  
The Given

In the network localization problem the goal is to determine the location of all nodes by using only partial information on the pairwise distances (and by computing the exact location of some nodes, called anchors). The network is said to be uniquely localizable if there is a unique set of locations consistent with the given data. Recent results from graph theory and combinatorial rigidity made it possible to characterize uniquely localizable networks in two dimensions. Based on these developments, extensions, related optimization problems, algorithms, and constructions also became tractable. This chapter gives a detailed survey of these new results from the graph theorist’s viewpoint.

scholarly journals A Modified Conjugacy Condition and Related Nonlinear Conjugate Gradient Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shengwei Yao ◽  
Xiwen Lu ◽  
Bin Qin
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Special Role ◽  
Conjugacy Condition ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient ◽  
The Given

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. In this paper, we propose a new conjugacy condition which is similar to Dai-Liao (2001). Based on this condition, the related nonlinear conjugate gradient method is given. With some mild conditions, the given method is globally convergent under the strong Wolfe-Powell line search for general functions. The numerical experiments show that the proposed method is very robust and efficient.

Distributed Parameter-Dependent Modeling and Control of Flexible Structures

2004 ◽  
Vol 127 (2) ◽  
pp. 230-239 ◽  
Author(s):  
Fen Wu ◽  
Suat E. Yildizoglu
Keyword(s):  
Optimization Problems ◽  
Flexible Structures ◽  
Synthesis Condition ◽  
Distributed Model ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Modeling And Control ◽  
L2 Norm ◽  
And Control ◽  
Parameter Dependent

In this paper, distributed parameter-dependent modeling and control approaches are proposed for flexible structures. The distributed model is motivated from distributed control design, which is advantageous in reducing control implementation cost and increasing control system reliability. This modeling approach mainly relies on a central finite difference scheme to capture the distributed nature of the flexible system. Based on the proposed distributed model, a sufficient synthesis condition for the design of a distributed output-feedback controller is presented using induced L2 norm as the performance criterion. The controller synthesis condition is formulated as linear matrix inequalities, which are convex optimization problems and can be solved efficiently using interior-point algorithms. The distributed controller inherits the same structure as the plant, which results in a localized control architecture and a simple implementation scheme. These modeling and control approaches are demonstrated on a non-uniform cantilever beam problem through simulation studies.

scholarly journals An interior point algorithm for solving linear optimization problems using a new trigonometric kernel function

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1471-1486
Author(s):  
S. Fathi-Hafshejani ◽  
Reza Peyghami
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Worst Case ◽  
Complexity Bounds ◽  
Linear Optimization Problems ◽  
Primal Dual ◽  
The Given

In this paper, a primal-dual interior point algorithm for solving linear optimization problems based on a new kernel function with a trigonometric barrier term which is not only used for determining the search directions but also for measuring the distance between the given iterate and the ?-center for the algorithm is proposed. Using some simple analysis tools and prove that our algorithm based on the new proposed trigonometric kernel function meets O (?n log n log n/?) and O (?n log n/?) as the worst case complexity bounds for large and small-update methods. Finally, some numerical results of performing our algorithm are presented.

scholarly journals DESIGN, SIMULATION AND MATHEMATICAL MODELLING OF THE DYNAMIC BEHAVIOR OF A VEHICLE TIRE AND CHASSIS SYSTEM AT A TURN.

2020 ◽  
Vol 7 (1) ◽  
pp. 12-23
Author(s):  
Mbelle Samuel Bisong ◽  
Paune Felix ◽  
Lokoue D. Romaric Brandon ◽  
Pierre Kisito Talla
Keyword(s):  
Road Construction ◽  
Maximum Speed ◽  
Safety Measures ◽  
The Road ◽  
Road Users ◽  
Road Section ◽  
Lateral Behavior ◽  
Road Characteristics ◽  
Fundamental Theorems ◽  
The Given

Road security has become with time a topic of concern in our society as per the increasing number of accidents and deaths occurring on the highways. Regulatory experts on road users have constantly been working for ways to solve this problem and thence better the lives of the citizens. This paper is aimed at proposing a mathematical model integrating specific parameters, describing the dynamic lateral behavior of a vehicle’s tire and chassis systems and enabling to state a relationship between road characteristics and vehicle dynamics. To achieve this, we made used of the fundamental theorems of dynamics for the modeling of the vehicle’s suspended and non-suspended masses and load transfers, then we associated this with the Pacejka Tire model to obtain a complete vehicle model. After the particularization of a global model, a simulator was realized named “DYNAUTO SIMULATOR” which iterates the given variables to produce a consistent result. After an experimental research made on the Ndokoti – PK 24 road section we could, thanks to our simulator determine the maximum speed to have at every turn of this road section and also understand the effect of the modification of a vehicle’s center of gravity on its stability. This work will be an important tool which can be recommended to the regulatory board as a major asset in the road construction policy and also in the improvement of road safety measures.

scholarly journals Vehicle Speed Information

2020 ◽  
Vol 5 (9) ◽  
pp. 867-868
Author(s):  
Vani Valsaraj
Keyword(s):  
Maximum Speed ◽  
Vehicle Speed ◽  
Road Accidents ◽  
Driving Speed ◽  
The Given ◽  
Present World

Road accidents have been very common in the present world with prime cause being careless driving. It is very necessary to identify the careless driver. However, with the advancement in the technology, different governing bodies are demanding some sort of computerized technology to control the driving speed of drivers. At this scenario, we are proposing system to detect vehicle speed been driven the given maximum speed of vehicles the respective roads or highway limits.

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