scholarly journals Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2386
Author(s):  
Andrey A. Galyaev ◽  
Pavel V. Lysenko ◽  
Evgeny Y. Rubinovich
Keyword(s):  
Stochastic Control ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Threshold Value ◽  
Optimal Stochastic Control ◽  
Control Law ◽  
Stochastic Problem ◽  
Deterministic Problem ◽  
Analytical Estimation ◽  
Suboptimal Solution

This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation.

scholarly journals A computational method for a class of jump linear quadratic systems

1995 ◽  
Vol 36 (4) ◽  
pp. 414-423
Author(s):  
K. H. Wong ◽  
N. Lock ◽  
K. Kaji
Keyword(s):  
Nonlinear Programming ◽  
Feedback Control ◽  
Stochastic Control ◽  
Optimization Problem ◽  
Original Problem ◽  
Computational Method ◽  
Control Law ◽  
Linear Quadratic ◽  
Programming Technique ◽  
Parameter Values

AbstractA class of linear systems subject to sudden jumps in parameter values is considered. To solve this class of stochastic control problem, we try to seek the best feedback control law depending only on the measurable output. Based on this idea, we convert the original problem into an approximate constrained deterministic optimization problem, which can be easily solved by any existing nonlinear programming technique. An example is solved to illustrate the efficiency of the method.

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

scholarly journals Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 303
Author(s):  
Nikolai Krivulin
Keyword(s):  
Decision Problem ◽  
Optimization Problem ◽  
Pareto Frontier ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Optimal Solution ◽  
Algebraic Solution ◽  
Pairwise Comparisons ◽  
Logarithmic Scale ◽  
Idempotent Algebra

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.

scholarly journals Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Serena Wang ◽  
Maya Gupta ◽  
Seungil You
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Combinatorial Optimization Problem ◽  
Joint Optimization ◽  
Early Stopping ◽  
Time Approximation ◽  
Approximation Bound ◽  
Evaluation Time ◽  
Speed Up ◽  
Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

Dynamic multi-objective matrix control for a class of switched systems

2021 ◽  
pp. 014233122199338
Author(s):  
Ali Thamallah ◽  
Anis Sakly ◽  
Faouzi M’Sahli
Keyword(s):  
Switched Systems ◽  
Optimization Problem ◽  
Control Method ◽  
Optimization Procedure ◽  
Control Law ◽  
Dynamic Matrix Control ◽  
General Reference ◽  
Multi Objective ◽  
Dynamic Matrix ◽  
Matrix Control

This article focuses on the tracking and stabilizing issues of a class of discrete switched systems. These systems are characterized by unknown switching sequences, a non-minimum phase, and time-varying or dead modes. In particular, for those governed by an indeterminate switching signal, it is very complicated to synthesize a control law able to systematically approach general reference-tracking difficulties. Taking into account the difficulty to express the dynamic of this class of systems, the present paper presents a new Dynamic matrix control method based on the multi-objective optimization and the truncated impulse response model. The formulation of the optimization problem aims to approach the general step-tracking issues under persistent and indeterminate mode changes and to overcome the stability problem along with retaining as many desirable features of the standard dynamic matrix control (DMC) method as possible. In addition, the formulated optimization problem integrates estimator variables able to manipulate the optimization procedure in favor of the active mode with an appropriate adjustment. It also provides a progressive and smooth multi-objective control law even in the presence of problems whether in subsystems or switching sequences. Finally, simulation examples and comparison tests are conducted to illustrate the potentiality and effectiveness of the developed method.

scholarly journals Robust Beamforming Design for Secure V2X Downlink System with Wireless Information and Power Transfer under a Nonlinear Energy Harvesting Model

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3294 ◽  
Author(s):  
Shidang Li ◽  
Chunguo Li ◽  
Weiqiang Tan ◽  
Baofeng Ji ◽  
Luxi Yang
Keyword(s):  
Energy Harvesting ◽  
Traffic Safety ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Base Station ◽  
Power Splitting ◽  
Power Transfer ◽  
Vehicular Communication ◽  
Downlink System ◽  
Nonlinear Energy

Vehicle to everything (V2X) has been deemed a promising technology due to its potential to achieve traffic safety and efficiency. This paper considers a V2X downlink system with a simultaneous wireless information and power transfer (SWIPT) system where the base station not only conveys data and energy to two types of wireless vehicular receivers, such as one hybrid power-splitting vehicular receiver, and multiple energy vehicular receivers, but also prevents information from being intercepted by the potential eavesdroppers (idle energy vehicular receivers). Both the base station and the energy vehicular receivers are equipped with multiple antennas, whereas the information vehicular receiver is equipped with a single antenna. In particular, the imperfect channel state information (CSI) and the practical nonlinear energy harvesting (EH) model are taken into account. The non-convex optimization problem is formulated to maximize the minimum harvested energy power among the energy vehicular receivers satisfying the lowest harvested energy power threshold at the information vehicular receiver and secure vehicular communication requirements. In light of the intractability of the optimization problem, the semidefinite relaxation (SDR) technique and variable substitutions are applied, and the optimal solution is proven to be tight. A number of results demonstrate that the proposed robust secure beamforming scheme has better performance than other schemes.

scholarly journals Topology Optimization of Automotive sheet metal part using Altair Inspire

2020 ◽  
Vol 5 (3) ◽  
pp. 143-150
Author(s):  
Netsanet Ferede
Keyword(s):  
Topology Optimization ◽  
Sheet Metal ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Sheet Metal Part ◽  
Metal Part ◽  
Solution Quality ◽  
Design Engineers ◽  
Automotive Sheet ◽  
Reduced Costs

In an optimization problem, different candidate solutions are compared with each other, and then the best or optimal solution is obtained which means that solution quality is fundamental. Topology optimization is used at the concept stage of design. It deals with the optimal distribution of material within the structure. Altair Inspire software is the industry's most powerful and easy-to-use Generative Design/Topology Optimization and rapid simulation solution for design engineers. In this paper Topology optimization is applied using Altair inspire to optimize the Sheet metal Angle bracket. Different results are conducted the better and final results are fulfilling the goal of the paper which is minimizing the mass of the sheet metal part by 65.9%  part and Maximizing the stiffness with Better Results of Von- Miss Stress Analysis,  Displacement, and comparison with different load cases.  This can lead to reduced costs, development time, material consumption, and product less weight.

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