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The max-out min-in problem: A tool for data analysis

COMPUTERS & OPERATIONS RESEARCH 2023年 154卷

作者： Cerdeira, Jorge Orestes Martins, Maria Joao Raydan, Marcos FCT NOVA Ctr Math & Applicat NovaMath P-2829516 Caparica Portugal FCT NOVA Dept Math P-2829516 Caparica Portugal Univ Lisbon Forest Res Ctr Sch Agr Tapada Ajuda P-1349017 Lisbon Portugal FCT NOVA Ctr Math & Applicat NovaMath P-2829516 Caparica Portugal

Consider a graph with vertex set V and non-negative weights on the edges. For every subset of vertices S , define phi(S) to be the sum of the weights of edges with one vertex in S and the other in V backslash S , minus the sum of the weights of the edges with both vertices in S. We consider the problem of finding S subset of C V for which phi(S) is maximized. We call this combinatorial optimization problem the max-out min-in problem (MOMIP). In this paper we (i) present a linear 0/1 formulation and a quadratic unconstrained binary optimization formulation for MOMIP;(ii) prove that the problem is NP-hard;(iii) report results of computational experiments on simulated data to compare the performances of the two models;(iv) illustrate the applicability of MOMIP for two different topics in the context of data analysis, namely in the selection of variables in exploratory data analysis and in the identification of clusters in the context of cluster analysis;and (v) introduce a generalization of MOMIP that includes, as particular cases, the well-known weighted maximum cut problem and a novel problem related to independent dominant sets in graphs.

关键词： Combinatorial optimization Weighted graphs quadratic programming Computational complexity Variable selection Cluster analysis

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Upright and Crawling Locomotion and Its Transition for a Wheel-Legged Robot

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MICROMACHINES 2022年第8期13卷 1252-1252页

作者： Qiu, Xuejian Yu, Zhangguo Meng, Libo Chen, Xuechao Zhao, Lingxuan Huang, Gao Meng, Fei Beijing Inst Technol Sch Mechatron Engn Beijing 100081 Peoples R China Minist Educ Key Lab Biomimet Robots & Syst Beijing 100081 Peoples R China Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China

To face the challenge of adapting to complex terrains and environments, we develop a novel wheel-legged robot that can switch motion modes to adapt to different environments. The robot can perform efficient and stable upright balanced locomotion on flat roads and flexible crawling in low and narrow passages. For passing through low and narrow passages, we propose a crawling motion control strategy and methods for transitioning between locomotion modes of wheel-legged robots. In practical applications, the smooth transition between the two motion modes is challenging. By optimizing the gravity work of the body, the optimal trajectory of the center of mass (CoM) for the transition from standing to crawling is obtained. By constructing and solving an optimization problem regarding the posture and motion trajectories of the underactuated model, the robot achieves a smooth transition from crawling to standing. In experiments, the wheel-legged robot successfully transitioned between the crawling mode and the upright balanced moving mode and flexibly passed a low and narrow passage. Consequently, the effectiveness of the control strategies and algorithms proposed in this paper are verified by experiments.

关键词： wheel-legged robot two locomotion modes mode transition quadratic programming

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A Modified Lagrange Method for Solving Convex quadratic Optimization Problems

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Open Journal of Optimization 2024年第1期13卷 1-20页

作者： Twum B. Stephen Avoka John Christian J. Etwire School of Mathematical Science C. K. Tedam University of Technology and Applied Sciences Navrongo Ghana Department of Mathematics University for Development Studies Tamale Ghana

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

关键词： quadratic programming Lagrangian Function Lagrange Multipliers Optimality Conditions Subsidiary Equations Modified Lagrange Method

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BEM Implementation of a Quasistatic and Rate-independent Non-associative Model of Mixed-mode Interface-crack Growth

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Procedia Materials Science 2014年 3卷 1191-1196页

作者： Vladislav Mantič Christos G. Panagiotopoulos Grupo de Elasticidad y Resistencia de Materiales Escuela Técnica Superior de Ingeniería Universidad de Sevilla Camino de los Descubrimientos s/n 41092 Sevilla Spain

The present authors and coworkers have recently developed a new physically and mathematically well justified and efficient approach for interface crack onset and propagation, implemented in finite and boundary element method (FEM and BEM) codes and applied to several problems of engineering interest. This approach borrows concepts from damage mechanics, such as the damage variable, from plasticity, as kinematic hardening, and from interface fracture mechanics, as fracture energy dependent on the fracture mode mixity. The computational implementation is based on recursive minimizations of a total energy functional, which can be computed by FEM and BEM. Global or specific local minimizations lead to different solution types, the energetic and stress driven solutions, respectively. In opposite to the associative models, where interface plasticity is explicitly taken into account by a plastic slip variable, applied to mixed-mode crack propagation problems by the present authors so far, it seems that non-associative models have the advantage of ending up at easier (e.g. smooth instead of non-smooth) and reduced (e.g. elimination of plasticity variable) minimization problems. An implementation of such a non-associative model in a collocation BEM code is presented and applied to an engineering problem of delamination.

关键词： adhesive contact interface damage rate-independent non-associative model boundary element method quadratic programming

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Control of Nonlinear Systems Subject to Input Constraints

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IFAC Proceedings Volumes 1995年第14期28卷 13-18页

作者： Simone L. de Oliveira Vesna Nevistić Manfred Morari California Institute of Technology Chemical Engineering Department 210-41 91125 Pasadena Automatic Control Laboratory Swiss Federal Institute of Technology (ETH) 8092 Zürich Switzerland

Two different approaches are investigated: (1) Model Predictive Control (MPC) utilizing a linear model resulting from a local linearization of the plant at each time step; and (2) Feedback Linearization (FL) with MPC in an outer loop to avoid constraint violations by the linearizing controller. In the latter case the constraints are generally nonlinear and the optimization problem must be solved in an iterative manner. These two techniques are compared in terms of their stability properties, the on-line effort and the relative performance on two practically motivated test examples.

关键词： Predictive control Nonlinear control systems Stability Robust control quadratic programming Optimization Lyapunov methods Constraint theory

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Optimizing battery discharge management of PMSM vehicles using adaptive nonlinear predictive control and a Generalized Integrator

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AIN SHAMS ENGINEERING JOURNAL 2024年第12期15卷

作者： Ismail, Moustafa Magdi Al-Dhaifallah, Mujahed Rezk, Hegazy Habib, Habib Ur Rahman Hamad, Samir A. King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Sustainable Energy Syst Dhahran 31261 Saudi Arabia Minia Univ Fac Engn Elect Engn Dept EL Minya 61517 Egypt King Fahd Univ Petr & Minerals Control & Instrumentat Engn Dept Dhahran 31261 Saudi Arabia Prince Sattam Bin Abdulaziz Univ Coll Engn Wadi Alddawasir Dept Elect Engn Al Kharj Saudi Arabia Univ Engn & Technol Taxila Fac Elect & Elect Engn Dept Elect Engn Taxila 47050 Pakistan Beni Suef Univ Fac Technol & Educ Dept Proc Control Technol Bani Suwayf Egypt

Electric vehicles (EVs) are key to a sustainable future, but extending battery life is essential to reduce costs and environmental impact. Thus, this paper presents the development of an Adaptive Nonlinear Predictive Model (ANLPM), integrated with a Third Order Generalized Integrator (TOGI) flux observer, which enhances induced torque estimation and stator reactance in Permanent Magnet Synchronous Motor (PMSM) systems. The model employs a Sequential quadratic programming (SQP) algorithm, ensuring numerical stability and efficiency within the Model Predictive Control (MPC) framework to handle nonlinear constraints effectively. Moreover, simulation results demonstrate that the ANLPM significantly outperforms classical Adaptive Linear Predictive Models (ALPM), Seven-Dimensional LPM (SDLPM), and Proportional-Integral (PI) control strategies. It achieves marked reductions in battery discharge current and energy consumption rates. Therefore, simulation comparisons, across different scenarios, show that ANLPM reduces battery discharge current by 3% over ALPM and 44.7% over PI, while cutting energy consumption by 12.2% and 28.2%, and decreasing parallel battery cells by 14.2% and 28%, respectively. Under high temperatures, ANLPM cuts battery consumption by 45.3% and reduces cells by 43.7% compared to SDLPM, highlighting its efficiency in managing energy and extending battery life in EVs.

关键词： ANLPM Adaptive Nonlinear Predictive Model ALPM Adaptive Linear Predictive Models DC Direct Current DP Dynamic programming EVs Electric Vehicles FEM Finite Element Method MPC Model Predictive Control MTPA Maximum Torque per Ampere PMSM Permanent Magnet Synchronous Motor PI Proportional Integral PWM Pulse Width Modulation QP quadratic programming RL Reinforcement Learning SQP Sequential quadratic programming SSE Steady State Error SDALPM Seven-dimensional adaptive linear predictive model TOGI Third Order Generalized Integrator VSI Voltage Source Inverter

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An Approximate Analysis of Quasi-Periodic Systems Via Floquet Theory

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JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS 2018年第2期13卷 021008-021008页

作者： Sharma, Ashu Sinha, S. C. Auburn Univ Dept Mech Engn Auburn AL 36849 USA

Parametrically excited linear systems with oscillatory coefficients have been generally modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquet theory. However, in many cases, the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. It is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquet theory. Based on this premise, a systematic approach has been developed and applied to three typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are very close to the exact boundaries of original quasi-periodic equations computed numerically using maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. In addition, state transition matrices (STMs) are also computed symbolically in terms of system parameters using Chebyshev polynomials and Picard iteration method. Stability diagrams based on this approach are found to be in excellent agreement with those obtained from numerical methods. The coefficients of parametric excitation terms are not necessarily small in all cases.

关键词： Stability quadratic programming Bifurcation Computation

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CONTINUOUS-TIME LQ PREDICTIVE POLE-PLACEMENT CONTROL

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IFAC Proceedings Volumes 2005年第1期38卷 359-364页

作者： Peter J Gawthrop Wen-Hua Chen Liuping Wang Centre for Systems and Control and Department of Mechanical Engineering University of Glasgow GLASGOW. G12 8QQ Scotland Department of Aeronautical and Automotive Engineering Loughborough University Leicestershire LE11 3TU UK Discipline of Electrical Energy and Control Systems School of Electrical and Computer Engineering RMIT University Melbourne Victoria 3000 Australia

The previously developed Predictive Pole Placement (PPP) controller is modified to give enhanced numerical and stability properties by embedding the method in a linear-quadratic formulation to give a linear-quadratic PPP (LQPPP) controller. Input, output and state constraints are considered using an natural quadratic programming (QP) formulation of LQPPP. Illustrative examples are given.

关键词： Predictive control pole-assignment constraint satisfaction problems quadratic programming continuous-time systems

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An Approach to QP-based Thrust Allocation considering Inflow ⁎

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IFAC-PapersOnLine 2021年第16期54卷 126-131页

作者： Philipp Koschorrek Martin Kosch J.M. Voith SE & Co. KG \ VTA 89522 Heidenheim Germany Institute of Automatic Control RWTH Aachen University 52074 Aachen Germany

One essential subtask in Dynamic Positioning is the optimal thrust distribution onto all available propulsors - the thrust allocation. Current thrust allocation algorithms support a variety of different propulsor types, but usually only under bollard pull conditions, hence ignoring water inflow. However, there are marine control tasks in which severe relative motion through water is present. In such conditions zero-inflow models may suggest wrong thrust vectors, which may lead to degraded positioning performance. In this paper an approach for dynamic thrust allocation is presented that utilizes available information on water inflow. The method is inspired by stochastic optimization and uses a set of achievable thrust points to construct convexified constraints for an underlying quadratic programming optimization algorithm. The workflow of the proposed method as well as simple simulations are shown on the example of thrust generation with cycloidal propellers.

关键词： Marine Systems Dynamic Positioning Dynamic Allocation Optimization quadratic programming

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Tubular Solution Styrene Polymerization Reactors: Modeling, Control and Stability Analysis

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IFAC Proceedings Volumes 1998年第11期31卷 697-702页

作者： M.P. Vega E.L. Lima J.C. Pinto Programa de Engenharia Química/COPPE Universidade Federal do Rio de Janeiro Rio de Janeiro - Brazil

A detailed model for a tubular polymerization reactor may be successfully replaced by a much simpler hybrid neural model (HNM), that can be used as the internal model in a model predictive control (MPC) strategy. However, HNMs, even allowing a satisfactory one step ahead prediction, may present incompatible general dynamic behavior, leading to improper closed loop responses. The reason for the undesired behavior seems to be related to the use of uncompleted data sets for the neural network (NN) learning process. This is an indication that, for each kind of process, the number and range of the data used in the learning process are of paramount importance.

关键词： Neural networks stability analysis hybrid models predictive control nonlinear control quadratic programming

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