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Quasi-finite-rank approximation of compression operators on L_∞[0, h) with application to stability analysis of time-delay systems

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IET CONTROL THEORY AND APPLICATIONS 2014年第2期8卷 77-85页

作者： Kim, Jung Hoon Hagiwara, Tomomichi Kyoto Univ Dept Elect Engn Nishikyo Ku Kyoto 6158510 Japan

This study discusses a new method for approximating compression operators, which play important roles in the operator-theoretic approach to sampled-data systems and time-delay systems. Stimulated by the success in the application of quasi-finite-rank approximation of compression operators defined on the Hilbert space L-2[0, h), the authors study a parallel problem for compression operators defined on the Banach space L[0, h). In spite of similarity between these problems, they are led to applying a completely different approach because of essential differences in the underlying spaces. More precisely, they apply the idea of the conventional fast-sample/fast-hold (FSFH) approximation technique, and show that the approximation problem can be transformed into such a linear programming problem that asymptotically leads to optimal approximation as the FSFH approximation parameter M tends to infinity. Finally, they demonstrate the effectiveness of the L[0, h)-based approximation technique through numerical examples, with particular application to stability analysis of time-delay systems.

关键词： approximation theory Banach spaces delay systems Hilbert spaces linear programming sampled data systems stability quasi-finite rank approximation compression operator stability analysis time delay system operator theory approach sampled data system Hilbert space L-2[0, h) parallel problem Banach space L-a[0, h) fast sample-fast hold FSFH approximation technique linear programming problem L-a[0, h)-based approximation technique

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Lexicographic Multiobjective Integer programming for Optimal and Structurally Minimal Petri Net Supervisors of Automated Manufacturing Systems

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2015年第11期45卷 1459-1470页

作者： Huang, Bo Zhou, MengChu Zhang, GongXuan Ammari, Ahmed Chiheb Alabdulwahab, Ahmed Fayoumi, Ayman G. Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing 210094 Jiangsu Peoples R China New Jersey Inst Technol Dept Elect & Comp Engn Newark NJ 07102 USA King Abdulaziz Univ Renewable Energy Res Grp Jeddah 21589 Saudi Arabia King Abdulaziz Univ Renewable Energy Res Grp Dept Elect & Comp Engn Jeddah 21589 Saudi Arabia Carthage Univ INSAT Inst MMA Lab Tunis 1080 Tunisia King Abdulaziz Univ Dept Informat Syst Jeddah 21589 Saudi Arabia

Based on Petri net (PN) models of automated manufacturing systems, this paper proposes a deadlock prevention method to obtain a maximally permissive (optimal) supervisor while minimizing its structure. The optimal supervisor can be achieved by forbidding all first-met bad markings (FBMs) and permitting all legal markings in a PN model. An FBM obtained via a single transition's firing at a legal marking is a deadlock or marking that inevitably evolves into a deadlock. A lexicographic multiobjective integer programming problem with multiple objectives to be achieved sequentially is formulated to design such an optimal and structurally minimal supervisor. As a nonlinear function, the quantity of its directed arcs is minimized. A conversion method is proposed to convert the nonlinear model into a linear one. With the premise that each place in the supervisor is associated with a nonnegative place invariant, the controlled net holds all legal markings of the net model, and the supervisor has the minimal structure. Finally, some examples are used to illustrate the application of the proposed approach.

关键词： Automated manufacturing system (AMS) deadlock prevention discrete event system linear programming problem Petri net (PN)

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A new approach to fuzzy part-family formation in cellular manufacturing systems

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2001年第8期18卷 591-597页

作者： Ravichandran, KS Rao, KCS Shanmugha Coll Engn Dept Math Thanjavur 613402 Tamil Nadu India Alagappa Univ Dept Math Karaikkudi Tamil Nadu India

Group technology (GT) is one of the major issues in successful implementation of cellular manufacturing systems. The success of GT implementation depends only on an effective formation of part-families. The effective formation of part-families depends mainly on an effective formation of a similarity coefficient measure. Many similarity coefficients have been produced over the past three decades, but better similarity coefficient measures are required. The decision-making process in a manufacturing system often involves uncertainties and ambiguities. Under such circumstances, fuzzy methodologies have proved to be effective tools for taking fuzziness into consideration. In this paper, we use fuzzy cluster analysis to form part-families and assign parts to existing part-families. We have established a new approach to convert a fuzzy clustering matrix into a zero-one incidence matrix. We have also developed a new similarity coefficient measure and this coefficient measure is used to form a part-family. A mathematical model that uses this similarity coefficient for solving optimally, the part-family formation problems in cellular manufacturing is developed. Finally, it is compared with other models by giving an illustration with a numerical example.

关键词： cellular manufacturing conventional clustering fuzzy clustering fuzzy set theory group technology linear programming problem part-family similarity coefficient

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BOTTLENECK linear-programming

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MATHEMATICAL programming 1976年第3期11卷 291-298页

作者： GARFINKEL, RS RAO, M UNIV TENNESSEE KNOXVILLETN 37916 UNIV ROCHESTER ROCHESTERNY 14627

The Bottleneck linear programming problem (BLP) is to maximizex0 = max j c j ,x j > 0 subject toAx = b, x ⩾ 0. A relationship between the BLP and a problem solvable by a “greedy” algorithm is established. Two alg... 详细信息

关键词： Mathematical Method programming problem Computational Experience linear programming problem

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SPECIAL SIMPLEX ALGORITHM FOR MULTI-SECTOR problemS

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NUMERISCHE MATHEMATIK 1968年第4期12卷 288-+页

作者： HEESTERMAN, AR Faculty of Commerce and Social Science University of Birmingham 15 Birmingham Great Britain

This paper describes a proposed special algorithm for a certain class of partionable linear programming problems. The matrix defining such a linear programming problem consists of a number of non-zero diagonal blocks,... 详细信息

关键词： Mathematical Method programming problem linear programming problem Special Algorithm Diagonal Block

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Automated synthesis of fixed structure QFT prefilter using piecewise linear approximation based linear programming optimization techniques

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IFAC-PapersOnLine 2016年第1期49卷 349-354页

作者： Nataraj, P.S.V. Makwana, Dipesh Systems and Control Engineering Group IIT Bombay India

Prefilter synthesis is one of the important design steps of Horowitz's quantitative feedback theory (QFT) to robust feedback system synthesis. The prefilter is designed to achieve tracking specifications. In this paper, a new, computationally efficient approach for automation of the prefilter design step is proposed. A linear programming based algorithm is proposed for the automatic synthesis of fixed structure QFT prefilter. In present work, prefilter synthesis problem is posed as a piecewise linear approximation based linear programming problem and solved with GUROBI optimizer *** proposed method is validated using a benchmark problem and a simple, low order prefilter is obtained in quick time. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Piecewise linear techniques Feedback linear programming Robust control Automatic synthesis Computationally efficient linear programming optimization linear programming problem Order sets Piecewise linear approximations Prefilter designs Quantitative feedback theory

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An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2024年第9期15卷 4370-4403页

作者： Kumar, P. Senthil Amity Univ Amity Sch Engn & Technol Bengaluru 562110 Karnataka India

It presents the type-2 intuitionistic fuzzy solid transportation problem (type-2 IFSTP) in a real-world situation and introduces an efficient technique based on software codes for solving type-2 IFSTP. It defines various types of intuitionistic fuzzy solid transportation problems (IFSTPs) and presents a mathematical model of full and type-2 IFSTPs. Additionally, the theorem, corollary, and their proof, as well as some results relevant to type-2 IFSTPs, are presented. Both the existing problem's solution and the proposed type-2 IFSTP's solution are compared using software (e.g., Matlab). In particular, solving IFSTPs using Matlab is new in the literature. Shortcomings in the existing results are pointed out and solved. Using the proposed approach, the optimal solution and optimal objective value of both the solid transportation problem (STP) and type-2 IFSTPs are obtained concurrently with one LP model, which is the key objective of this article. It also discusses the time complexity of the existing algorithms for solving STPs with different intuitionistic fuzzy numbers (IFNs). Both the proposed results and the benefits of the proposed methodology are thoroughly discussed. Finally, a sound conclusion and future research directions are provided.

关键词： Type-2 intuitionistic fuzzy solid transportation problem linear programming problem Matlab Solution Software PSK theorem

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Cooperation among liquefied natural gas suppliers: Is rationalization the sole objective?

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ENERGY ECONOMICS 2010年第4期32卷 933-947页

作者： Massol, Olivier Tchung-Ming, Stephane IFP Sch Ctr Econ & Management F-92852 Rueil Malmaison France City Univ London Dept Econ London EC1V 0HB England IFP Econ Studies Div F-92852 Rueil Malmaison France Univ Montpellier I CREDEN F-34054 Montpellier France

This paper examines the development of cooperative strategies between countries exporting Liquefied Natural Gas (LNG) and members of the Gas Exporting Countries Forum (GECF). This economic study focuses specifically on an often-raised scenario: the emergence of a cooperative approach designed with the sole aim of logistic rationalization, and which would not have any effect on LNG prices. We first assess the annual gains that may result from this market-power-free cooperative approach using a simple static transportation model. The numerical results obtained suggest that, in the absence of a gain redistribution policy, this cooperative strategy will probably not be adopted because cooperation would not be a rational move for some exporters. The problem of gain sharing is then formulated using cooperative game theory concepts. Several gain-sharing methods have been studied, including the Shapley value and various nucleolus-inspired concepts. Our results suggest that the choice of a redistribution policy appears relatively restricted. Out of the methods studied, only one - per capita nucleolus - satisfies two key requirements: core belonging and monotonicity (in the aggregate). Lastly, we look at how cooperation may give rise to a coordination cost and try to determine the maximum amount of this cost. In view of the low level of this amount and the relative complexity of the sharing method implemented, we consider that the credibility of a logistic cooperation scenario exempt from market power should be reappraised. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Liquefied natural gas Cooperative game theory linear programming problem

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Mathematical Model to Evaluate the Impact of Power Supply Constraint for Electric Vehicles on Transportation Network

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INTERNATIONAL JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS RESEARCH 2024年第1期23卷 16-28页

作者： Nakajima, Yuki Shimamoto, Hiroshi Univ Miyazaki Grad Sch Engn 1-1 Gakuen Kibanadai Nishi Miyazaki Japan Univ Miyazaki Dept Civil & Environm Engn 1-1 Gakuen Kibanadai Nishi Miyazaki Japan

This paper proposes the UE-based mathematical model to evaluate driver's choice of vehicle types and paths, explicitly considering the supply power constraint in addition to the charging station capacity constraints. Because the flows of EVs in the proposed model are represented in a path-based manner, we apply a column generation-based algorithm to avoid enumerating all of the possible paths. The contributions of this study are that 1) we consider both pre-trip charging and charging during a trip, and that 2) we focus on the difference in the impact of power supply constraints on vehicles that need to charge during a trip and those that do not. The proposed model is applied to a hypothetical network. As a result, we confirmed that 1) while the share of EVs in the middle distance tends to be higher, the share of EVs in the short and long distances tends to be lower, and that 2) in case of inadequate power supply, the share of EVs in the short and middle distances decreases significantly, whereas the share of EVs remains almost unchanged in long OD.

关键词： Electric Vehicle Mode and Path Choice Power Supply Constraint linear programming problem Column Generation Approach

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Calculation of Phase Equilibria of Pure Light Hydrocarbons Using the PC-SAFT Equation of State and the Direct Energy Minimisation

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MOSCOW UNIVERSITY PHYSICS BULLETIN 2023年第6期78卷 876-886页

作者： Isaeva, A. V. Bevzo, M. O. Lomonosov Moscow State Univ Fac Phys Dept Phys Earth Moscow 119991 Russia

In the oil and gas industry, there is growing interest in using the PC-SAFT equation of state for predicting the phase behaviour and physical properties of hydrocarbons. This article demonstrates how this equation of state can be used in combination with the direct energy minimisation algorithm of an isochoric-isothermal system for calculating vapour-liquid equilibrium parameters of hydrocarbons. The proposed approach is tested on four substances: methane, ethane, propane, and n-butane.

关键词： direct energy minimisation algorithm PC-SAFT equation of state Peng-Robinson equation of state linear programming problem

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