On asymptotically stabilizing control of nonlinear fractional control systems using an optimization scheme

2021 ◽  
pp. 014233122110056
Author(s):  
Mina Yavari ◽  
Alireza Nazemi
Keyword(s):  
Learning Algorithm ◽  
Error Function ◽  
Minimum Principle ◽  
Dynamic Control ◽  
Infinite Horizon ◽  
Unconstrained Minimization ◽  
Pontryagin Minimum Principle ◽  
Control Functions ◽  
Stabilizing Control ◽  
Fractional Control

In this paper, stabilization of the nonlinear fractional order systems with unknown control coefficients is considered where the dynamic control system depends on the Caputo fractional derivative. Related to the nonlinear fractional control (NFC) system, an infinite-horizon optimal control (OC) problem is first proposed. It is shown that the obtained OC problem can be an asymptotically stabilizing control for the NFC system. Using the help of an approximation, the Caputo derivative is replaced with the integer order derivative. The achieved infinite-horizon OC problem is then converted into an equivalent finite-horizon one. According to the Pontryagin minimum principle for OC problems and by constructing an error function, an unconstrained minimization problem is defined. In the optimization problem, trial solutions are used for state, costate and control functions where these trial solutions are constructed by using a two-layered perceptron neural network. A learning algorithm with convergence properties is also provided. Two numerical results are introduced to explain the main results.

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

scholarly journals Application and benchmarking of a direct method to optimize the fuel consumption of a diesel electric locomotive

2018 ◽  
Vol 232 (9) ◽  
pp. 2272-2289 ◽  
Author(s):  
V Macian ◽  
C Guardiola ◽  
B Pla ◽  
A Reig
Keyword(s):  
Optimal Control ◽  
Direct Method ◽  
Minimum Principle ◽  
Optimization Technique ◽  
Direct Methods ◽  
Optimization Methods ◽  
Computational Time ◽  
Electric Locomotive ◽  
Pontryagin Minimum Principle ◽  
A Direct Method

This paper addresses the optimal control of a long-haul passenger train to deliver minimum-fuel operations. Contrary to the common Pontryagin minimum principle approach in railroad-related literature, this work addresses this optimal control problem with a direct method of optimization, the use of which is still marginal in this field. The implementation of a particular direct method based on the Euler collocation scheme and its transcription into a nonlinear problem are described in detail. In this paper, this optimization technique is benchmarked with well-known optimization methods in the literature, namely dynamic programming and the Pontryagin minimum principle, by simulating a real route. The results showed that the direct methods are on the same level of optimality compared with other algorithms while requiring reduced computational time and memory and being able to handle very complex dynamic systems. The performance of the direct method is also compared to the real trajectory followed by the train operator and exhibits up to 20% of fuel saving in the example route.

Significant of Gradient Boosting Algorithm in Data Management System

2021 ◽  
Vol 9 (2) ◽  
pp. 85-100
Author(s):  
Md Saikat Hosen ◽  
Ruhul Amin
Keyword(s):  
Data Management ◽  
Text Classification ◽  
Learning Process ◽  
Learning Algorithm ◽  
Error Function ◽  
Data Management System ◽  
Gradient Boosting ◽  
Response Parameter ◽  
Boosting Algorithms ◽  
Boosting Algorithm

Gradient boosting machines, the learning process successively fits fresh prototypes to offer a more precise approximation of the response parameter. The principle notion associated with this algorithm is that a fresh base-learner construct to be extremely correlated with the “negative gradient of the loss function” related to the entire ensemble. The loss function's usefulness can be random, nonetheless, for a clearer understanding of this subject, if the “error function is the model squared-error loss”, then the learning process would end up in sequential error-fitting. This study is aimed at delineating the significance of the gradient boosting algorithm in data management systems. The article will dwell much the significance of gradient boosting algorithm in text classification as well as the limitations of this model. The basic methodology as well as the basic-learning algorithm of the gradient boosting algorithms originally formulated by Friedman, is presented in this study. This may serve as an introduction to gradient boosting algorithms. This article has displayed the approach of gradient boosting algorithms. Both the hypothetical system and the plan choices were depicted and outlined. We have examined all the basic stages of planning a specific demonstration for one’s experimental needs. Elucidation issues have been tended to and displayed as a basic portion of the investigation. The capabilities of the gradient boosting algorithms were examined on a set of real-world down-to-earth applications such as text classification.

scholarly journals Development of Global Optimization Algorithm for Series-Parallel PHEV Energy Management Strategy Based on Radau Pseudospectral Knotting Method

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3268
Author(s):  
Kegang Zhao ◽  
Jinghao Bei ◽  
Yanwei Liu ◽  
Zhihao Liang
Keyword(s):  
Global Optimization ◽  
Energy Management ◽  
Computational Efficiency ◽  
Management Strategy ◽  
Hybrid Electric Vehicles ◽  
Minimum Principle ◽  
Management Strategies ◽  
Energy Management Strategy ◽  
Pontryagin Minimum Principle ◽  
Component Sizing

The powertrain model of the series-parallel plug-in hybrid electric vehicles (PHEVs) is more complicated, compared with series PHEVs and parallel PHEVs. Using the traditional dynamic programming (DP) algorithm or Pontryagin minimum principle (PMP) algorithm to solve the global-optimization-based energy management strategies of the series-parallel PHEVs is not ideal, as the solution time is too long or even impossible to solve. Chief engineers of hybrid system urgently require a handy tool to quickly solve global-optimization-based energy management strategies. Therefore, this paper proposed to use the Radau pseudospectral knotting method (RPKM) to solve the global-optimization-based energy management strategy of the series-parallel PHEVs to improve computational efficiency. Simulation results showed that compared with the DP algorithm, the global-optimization-based energy management strategy based on the RPKM improves the computational efficiency by 1806 times with a relative error of only 0.12%. On this basis, a bi-level nested component-sizing method combining the genetic algorithm and RPKM was developed. By applying the global-optimization-based energy management strategy based on RPKM to the actual development, the feasibility and superiority of RPKM applied to the global-optimization-based energy management strategy of the series-parallel PHEVs were further verified.

Formulations about Dynamics of Mobile Robots

2010 ◽  
Vol 166-167 ◽  
pp. 309-314 ◽  
Author(s):  
Iuliu Negrean ◽  
Claudiu Schonstein ◽  
Kalman Kacso ◽  
Calin Negrean ◽  
Adina Duca
Keyword(s):  
Kinetic Energy ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Dynamic Control ◽  
Nonholonomic Constraints ◽  
The Other ◽  
Robot Motion ◽  
Mobile Platforms ◽  
Control Functions ◽  
New Concepts

In this paper the dynamics equations for a mobile robot, named PatrolBot, will be developed, using new concepts in advanced mechanics, based on important scientific researches of the main author, concerning the kinetic energy. In keeping the fact that the mathematical models of the mobile platforms are different besides the other robots types, due to nonholonomic constraints, these dynamic control functions, will be computed, according to these restrictions for robot motion.

scholarly journals Convergence Analysis of An Improved Extreme Learning Machine Based on Gradient Descent Method

2016 ◽  
Vol 8 (1) ◽  
pp. 5-15
Author(s):  
Liu Yusong ◽  
Su Zhixun ◽  
Zhang Bingjie ◽  
Gong Xiaoling ◽  
Sang Zhaoyang
Keyword(s):  
Extreme Learning Machine ◽  
Learning Algorithm ◽  
Error Function ◽  
Gradient Descent Method ◽  
Testing Time ◽  
Training Procedure ◽  
Feed Forward Neural Network ◽  
Learning Machine ◽  
Theoretical Results ◽  
Hidden Nodes

Abstract Extreme learning machine (ELM) is an efficient algorithm, but it requires more hidden nodes than the BP algorithms to reach the matched performance. Recently, an efficient learning algorithm, the upper-layer-solution-unaware algorithm (USUA), is proposed for the single-hidden layer feed-forward neural network. It needs less number of hidden nodes and testing time than ELM. In this paper, we mainly give the theoretical analysis for USUA. Theoretical results show that the error function monotonously decreases in the training procedure, the gradient of the error function with respect to weights tends to zero (the weak convergence), and the weight sequence goes to a fixed point (the strong convergence) when the iterations approach positive infinity. An illustrated simulation has been implemented on the MNIST database of handwritten digits which effectively verifies the theoretical results..

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