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8th IEEE International Conference on Awareness Science and Technology (iCAST)

作者： Horng, Shih-Cheng Lin, Shieh-Shing Chaoyang Univ Technol Dept Comp Sci & Informat Engn Taichung Taiwan St Johns Univ Dept Elect Engn Taipei Taiwan

ISBN: (纸本)9781538629659

In this work, a two-stage approach is proposed for solving a class of quadratic programming problems containing Continuous and Discrete control variables (QPCD). In the first-stage, a heuristic search technique was used to choose N excellent solutions from entire solution space. In the second-stage, the sensitivity theory was utilized to evaluate the N excellent solutions and pick the top s solutions to build the candidate subset. These s candidate solutions in the candidate subset were evaluated using the exact model. The Ordinal Optimization theory showed that the optimal solution chosen from candidate subset belongs to the good enough solution with high probability. The proposed approach was compared with the traditional Lagrange relaxing method for solving the IEEE 30-bus power systems. The performances were evaluated by two compared indexes, Time Reducing Index and Objective value Reducing Index. Test results demonstrate that the proposed approach outperforms the traditional Lagrange relaxing method.

关键词： Ordinal optimization quadratic programming problem continuous and discrete control variables successive quadratic programming lagrange relaxation sensitivity analysis

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A class of continuous quadratic programming problems

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Unternehmensforschung Operations Research - Recherche Opérationnelle 1970年第1期14卷 220-227页

作者： Gogia, N.K. Gupta, R.P. Department of Mathematics Indian Institute of Technology Kanpur India

The present paper deals with some duality relations of a class of continuous quadratic programming problems. The analysis is developed by use of technique of Dorn for quadratic programming problems. © 1970 Physic... 详细信息

关键词： programming problem quadratic programming quadratic programming problem Present Paper Deal Duality Relation

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A proposed numerical solution of a class of fuzzy quadratic programming problems 2

A proposed numerical solution of a class of fuzzy quadratic ...

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2nd International Conference on Distributed Computing and High Performance Computing (DCHPC)

作者： Mazarei, Mohammad Mehdi Behroozpoor, Ali Asghar Kamyad, Ali Vahidian Islamic Azad Univ Bushehr Branch Dept Sci Bushehr Iran Ferdowsi Univ Mashad Dept Appl Math Mashhad Iran

ISBN: (纸本)9781665496728

In the real applied optimization problems, we usually face nonlinear fuzzy programming problems (FNLPPs). This paper focuses on a class of fuzzy quadratic programming problems (FQPPs) in which all of technical coefficients and constraint inequalities are fuzzy ones. Initially, some definitions of fuzzy mathematics are introduced and then, we discuss on fuzzy quadratic programming problems and introduce a new approach to find the approximate solution to these problems. Finally, we introduce some numerical examples to show the efficiency of the proposed approach.

关键词： Fuzzy quadratic programming problem Piecewise linearization

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On inexact quadratic programming problems involving mixed terms with an application to tea industry

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COMPUTERS & INDUSTRIAL ENGINEERING 2021年 156卷 107264-107264页

作者： Mahajan, Sumati Gupta, S. K. Punjab Engn Coll Dept Appl Sci Chandigarh 160012 India Indian Inst Technol Dept Math Roorkee 247667 Uttar Pradesh India

Inexact quadratic programming (IQP) is designed to handle impreciseness in data/modelling parameters of quadratic programming (QP). The nature of IQP often leads to procedural and applicability problems. The existing studies on IQP have not incorporated the terms of the type x(i)x(j), i not equal j in the formulation of IQP problem (or IQPP), thereby limiting its scope of applications to specific types of problems only. The paper presents an extension of the past efforts by including such terms and hence, gives wider scope of its applications. Two methodologies viz. Duality approach and Modified method to solve the generalized IQPP are suggested. In addition, it has been shown that the Modified method significantly increases the computational efficiency by reducing the involved variables and constraints. Finally, an application of IQP is demonstrated by citing a realistic problem from an area of product mix and production planning, particularly in the tea industry.

关键词： Inexact parameters quadratic programming problem Duality approach Modified method Convex optimization

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Computation of maximal turning points to nonlinear equations by nonsmooth optimization

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OPTIMIZATION METHODS & SOFTWARE 2016年第1期31卷 1-23页

作者： Il'yasov, Yavdat Ivanov, Aleksandr RAS Inst Math Ufa Russia Bashkir State Univ Fac Math & Informat Technol Ufa 450074 Russia

We develop a new approach to finding bifurcations of solutions of nonlinear equation systems, which is based on the detection of extreme values of a new type of variational functional associated with the considered problems. The variational functional is obtained constructively by the extended functional method which can be applied to a wide class of parametric problems including nonlinear partial differential equations. Sufficient and necessary conditions for the existence of a maximal turning point by the approach are proved. Based on these, an algorithm of the quasi-direction of steepest ascent is introduced. Simulation experiments are used to illustrate the behaviour of the method and to discuss its advantages and disadvantages in comparison with the alternatives.

关键词： turning point steepest ascent direction nonlinear system nonsmooth optimization quadratic programming problem

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MPC policy learning using DNN for human following control without collision

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ADVANCED ROBOTICS 2018年第3期32卷 148-159页

作者： Hirose, N. Tajima, R. Sukigara, K. Toyota Cent Res & Dev Labs Inc Nagakute Aichi Japan

Model predictive control has recently been applied to a wide variety of motion control systems. Model predictive control can be used to generate optimized control inputs with excellent performance considering inequality constraints to the control inputs, control outputs, and state variables. However, the computational load for this method is too heavy for implementation in most actual systems because the quadratic programming problem must be solved within the sampling period. As the number of inequality constraints, control variables, and state variables in the control system increases, more calculation time is required. In this study, a deep neural network designed to learn the model predictive control policy was developed to reduce the computational load. It is expected that a relatively small neural network can be used to learn the model predictive control policy. In the proposed system, the motion controller calculates the learned neural network in real time instead of solving the quadratic programming problem, realizing almost the same control performance as the original model predictive control approach. The effectiveness of the proposed approach was verified by applying it to the control of a personal robot designed to follow the user, which can provide daily support to the elderly. In Matlab simulations, the calculation time for the proposed approach was approximately times faster than that of the conventional method of solving the quadratic programming problem. In addition, an experiment using an actual personal robot was conducted to confirm the control performance.

关键词： Model predictive control deep learning neural network quadratic programming problem optimization

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Dual possibilistic regression analysis using support vector networks

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FUZZY SETS AND SYSTEMS 2020年 387卷 1-34页

作者： Hao, Pei-Yi Natl Kaohsiung Univ Sci & Technol Dept Informat Management 415 Chien Kung Rd Kaohsiung 807 Taiwan

This study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine (SVM) theory. The dual regression model, which comprises an upper model and a lower model, approximates the observed fuzzy phenomena from the outside and inside directions, respectively, such that the inclusion relationship between those two models holds. The proposed dual regression model better explains the inherent vagueness that exists in a given dataset. It provides the outer and inner bounds for the estimated vagueness region, and allows an estimation of the degree of confidence in the predicted fuzzy output. Using the principles for a twin support vector machine (TSVM), the upper- and lower models are estimated by solving two smaller SVM-type quadratic programming problems (QPPs), instead of a single larger QPP. This strategy significantly increases the learning speed for the proposed algorithm. The structural risk minimization principle of SVM makes the proposed method to yield better generalization ability. The kernel function method offers a model-independent framework for the proposed dual regression model. This paper focuses on the class of radial kernels, which enables the proposed method to conquer the problem of increasing spreads. The radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs. The experimental results verify the effectiveness and efficiency of the proposed method. In comparison with previous SVM-based dual regression model, the proposed approach significantly improves the sparsity, prediction speed, and training speed. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Fuzzy regression analysis Dual regression models Trapezoid fuzzy numbers Support vector machines Support vector regression machines quadratic programming problem

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Nonlinear temperature regulation of solar collectors with a fast adaptive polytopic LPV MPC formulation

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SOLAR ENERGY 2020年 209卷 214-225页

作者： Pipino, Hugo A. Morato, Marcelo M. Bernardi, Emanuel Adam, Eduardo J. Normey-Rico, Julio E. Univ Tecnol Nacl Appl Control & Embedded Syst Res Grp AC&ES RG San Francisco Argentina Univ Fed Santa Catarina Dept Automacao & Sistemas Renewable Energy Res Grp GPER Florianopolis SC Brazil Univ Nacl Litoral Fac Ingn Quim Santa Fe Argentina

Temperature control in solar collectors is a nonlinear problem: the dynamics of temperature rise vary according to the fluid flowing through the collector and to the temperature gradient along the collector area. In this way, this work investigates the formulation of a Model Predictive Control (MPC) application developed within a Linear Parameter Varying (LPV) formalism, which serves as a model of the solar collector process. The proposed system is an adaptive MPC, developed with terminal set constraints and considering the scheduling polytope of the model. At each instant, two quadratic programming (QPs) programs are solved: the first considers a backward horizon of N steps to find a virtual model-process tuning variable that defines the best LTI prediction model, considering the vertices of the polytopic system;then, the second QP uses this LTI model to optimize performances along a forward horizon of N steps. The paper ends with a realistic solar collector simulation results, comparing the proposed MPC to other techniques from the literature (linear MPC and robust tube-MPC). Discussions regarding the results, the design procedure and the computational effort for the three methods are presented. It is shown how the proposed MPC design is able to outrank these other standard methods in terms of reference tracking and disturbance rejection.

关键词： Model predictive control Linear parameter varying systems quadratic programming problem Tube MPC Solar collector

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Two-parameter Kautz network-based LTV-MPC for non-linear standalone micro-grid control

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IET RENEWABLE POWER GENERATION 2020年第12期14卷 2221-2231页

作者： Puvvula, Vidyasagar Verma, Pranjal Pragya Kesanakurthy, Shanti Swarup Indian Inst Technol Dept Elect Engn Chennai Tamil Nadu India

This study proposes a novel linear time-variant model predictive controller (LTV-MPC) for the centralised control of non-linear standalone micro-grids. At each sample, within the prediction horizon, LTV-MPC linearises the non-linear micro-grid model around the state and input reference trajectories resulting in a linear time-variant (LTV) model. The LTV model is used for predicting the forced response of the micro-grid. The natural response is predicted by solving the non-linear model along the state and input reference trajectories. An optimal control problem for the LTV-MPC is formulated using the complete predicted response, which is a quadratic programming problem instead of a non-convex non-linear programming problem. The quadratic programming problem is solved online at each sample to generate the optimal control trajectories within the control horizon. The study recommends the use of two-parameter orthonormal Kautz networks in the LTV-MPC design for the control trajectories approximation. The approximation drastically reduces the number of optimising variables in the optimal control problem without compromising LTV-MPC performance. A standalone eight bus micro-grid with one synchronous distributed generator (DG) and one photovoltaic-DG is considered for the analysis. The LTV-MPC performance is assessed for the different load disturbance and source intermittency scenarios. The results are compared with the existing MPC designs.

关键词： distributed power generation predictive control optimal control time-varying systems quadratic programming approximation theory linear systems linear programming nonlinear control systems parameter Kautz network-based LTV-MPC nonlinear standalone microgrid control linear time-variant model centralised control nonlinear standalone microgrids prediction horizon microgrid model LTV model forced response natural response nonlinear model input reference trajectories optimal control problem complete predicted response quadratic programming problem nonconvex nonlinear programming problem optimal control trajectories control horizon two-parameter orthonormal Kautz networks LTV-MPC design control trajectories approximation LTV-MPC performance standalone eight bus microgrid MPC designs

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Constrained generalised minimum variance controller design using projection-based recurrent neural network

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IET CONTROL THEORY AND APPLICATIONS 2017年第2期11卷 143-154页

作者： Toshani, Hamid Farrokhi, Mohammad Alipouri, Yousef Iran Univ Sci & Technol Sch Elect Engn Farjam St Tehran 16846 Iran

In this study, a generalised minimum variance control (GMVC) method using the projection-based recurrent neural network (PRNN) is proposed to minimise the error variance in the output of the non-linear plant. One the main drawbacks of the conventional GMVC approaches is the lack of a systematic procedure to deal with the input constraints. In this study, the PRNN is employed for incorporating the input constraints to the minimum variance index. This network is based on the optimality conditions of a constrained problem and is designed using projection theorem. To formulate the proposed approach, by considering an ARMAX model of the system and converting the cost function to a quadratic programming problem, the dynamics and output equations of the PRNN is obtained. The stability and global convergence of the PRNN is analytically shown. Moreover, suitable conditions for the weighting matrices of the cost function are determined to ensure the closed-loop stability. The proposed control method is applied to the non-linear quadruple tank and a comparative analysis between MVC, GMVC and the proposed approach is performed.

关键词： control system synthesis recurrent neural nets neurocontrollers nonlinear control systems optimal control quadratic programming matrix algebra convergence closed loop systems stability constrained generalised minimum variance controller design GMVC method projection-based recurrent neural network PRNN error variance minimisation nonlinear plant systematic procedure minimum variance index optimality conditions ARMAX model cost function quadratic programming problem weighting matrices closed-loop stability nonlinear quadruple tank comparative analysis global convergence

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