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potential function-based path-following control of an autonomous underwater vehicle in an obstacle-rich environment

TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2017年第8期39卷 1236-1252页

作者： Sahu, Basant Kumar Subudhi, Bidyadhar Natl Inst Sci & Technol Dept Elect Engn Berhampur 761008 Orissa India Natl Inst Technol Dept Elect Engn Rourkela India

This paper presents the development of simple but powerful path-following and obstacle-avoidance control laws for an underactuated autonomous underwater vehicle (AUV). potential function-based proportional derivative (PFPD) as well as a potential function-based augmented proportional derivative (PFAPD) control laws are developed to govern the motion of the AUV in an obstacle-rich environment. For obstacle avoidance, a mathematical potential function is used, which formulates the repulsive force between the AUV and the solid obstacles intersecting the desired path. Numerical simulations are carried out to study the efficacy of the proposed controllers and the results are observed. To reduce the values of the overshoots and steady-state errors identified due to the application of PFPD controller a PFAPD controller is designed that drives the AUV along the desired trajectory. From the simulation results, it is observed that the proposed controllers are able to drive the AUV to track the desired path, avoiding the obstacles in an obstacle-rich environment. The results are compared and it is observed that the PFAPD outperforms the PFPD to drive the AUV along the desired trajectory. It is also proved that it is not necessary to employ highly complicated controllers for solving obstacle-avoidance and path-following problems of underactuated AUVs. These problems can be solved with the application of PFAPD controllers.

关键词： Lyapunov's stability criterion obstacle avoidance path following potential function underactuated AUV

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potential function estimates for quasi-Einstein metrics

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JOURNAL OF functionAL ANALYSIS 2014年第7期267卷 1986-2004页

作者： Wang, Lin Feng Nantong Univ Sch Sci Nantong 226007 Peoples R China

In this paper, we derive the growth pinching estimates for potential functions of tau-quasi-Einstein metrics on complete noncompact connected manifolds, based on the estimates for the scalar curvature and the using of the weighted measure comparison theorem. Our results show that the estimates for potential functions rely on the sign of constants lambda and mu. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Quasi-Einstein metric Weighted measure potential function Growth pinching estimate

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potential function-BASED FRAMEWORK FOR MINIMIZING GRADIENTS IN CONVEX AND MIN-MAX OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2022年第3期32卷 1668-1697页

作者： Diakonikolas, Jelena Wang, Puqian Univ Wisconsin Dept Comp Sci 1210 W Dayton St Madison WI 53706 USA

Making the gradients small is a fundamental optimization problem that has eluded unifying and simple convergence arguments in first-order optimization, so far primarily reserved for other convergence criteria, such as reducing the optimality gap. In particular, while many different potential function-based frameworks covering broad classes of algorithms exist for optimality gap-based convergence guarantees, we are not aware of such general frameworks addressing the gradient norm guarantees. To fill this gap, we introduce a novel potential function-based framework to study the convergence of standard methods for making the gradients small in smooth convex optimization and convex-concave min-max optimization. Our framework is intuitive and provides a lens for viewing algorithms that makes the gradients small as being driven by a trade-off between reducing either the gradient norm or a certain notion of an optimality gap. On the lower bounds side, we discuss tightness of the obtained convergence results for the convex setup and provide a new lower bound for minimizing norm of cocoercive operators that allows us to argue about optimality of methods in the min-max setup.

关键词： gradient minimization convergence analysis potential function

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potential function OF INTERNAL-ROTATION OF (CH3)2CCLNO, CH3CCL2NO, AND THEIR DEUTERIUM ANALOGS

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BULLETIN OF THE ACADEMY OF SCIENCES OF THE USSR DIVISION OF CHEMICAL SCIENCE 1990年第3期39卷 476-480页

作者： TREPALIN, SV YARKOV, AV SOKOLOV, VB IVANOV, AN 1. Institute of Physiologically Active Substances Academy of Sciences of the USSR Chernogolovka

The potential function has been constructed for internal rotation of the NO-group in (CH3)2CClNO, CH3CCl2NO, and their deuterium analogs. It has been established that the N=O bond in the cisCl conformer of CH3CCl2NO does not eclipse the C-Cl bond, rather forming an angle of approximately 30?. It has been shown that a change in substitutent on the α-carbon atom may produce a substantial change in the form of the potential function of internal rotation (PFIR) of the NO group.

关键词： deuterium Analog Analog potential function Internal rotation Substantial change

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potential function of simplified protein models for discriminating native proteins from decoys: Combining contact interaction and local sequence-dependent geometry

Potential function of simplified protein models for discrimi...

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26th Annual International Conference of the IEEE-Engineering-in-Medicine-and-Biology-Society

作者： Zhang, JF Chen, R Liang, J Univ Illinois Dept Bioengn Chicago IL USA

ISBN: (纸本)0780384393

An effective potential function is critical for protein structure prediction and folding simulation. For simplified models of proteins where coordinates of only C,, atoms need to be specified, an accurate potential function is important. Such a simplified model is essential for efficient search of conformational space. In this work, we present a formulation of potential function for simplified representations of protein structures. It is based on the combination of descriptors derived from residue-residue contact and sequence-dependent local geometry. The optimal weight coefficients for contact and local geometry is obtained through optimization by maximizing margins among native and decoy structures. The latter are generated by chain growth and by gapless threading. The performance of the potential function in blind test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. This potential function have comparable or better performance than several residue-based potential functions that require in addition coordinates of side chain centers or coordinates of all side chain atoms.

关键词： decoy discrimination potential function protein structure prediction simplified protein models

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Determination of potential function for uncoupled-plane contact problems

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MATERIALS & DESIGN 2008年第4期29卷 818-828页

作者： Adibnazari, S. Sharafbafi, F. Naderl, D. Sharif Univ Technol Dept Aerosp Engn Tehran Iran

In this paper, the elastic contact problem of an asymmetrical shallow wedge with a half-plane is considered. The potential function of the contact problem has been obtained through a simple approach. This approach simplifies the routine method of determination of potential functions in elastic contact problems. Then this approach was utilized to solve the aforementioned geometry under frictionless and frictional condition. Utilization of the new relation not only simplifies the procedure of solving contact problems but also is very helpful for fretting fatigue studies. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： contact mechanics potential function asymmetrical wedge

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A new contact detection method for arbitrary dilated polyhedra with potential function in discrete element method

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2020年第24期121卷 5742-5765页

作者： Liu, Lu Ji, Shunying Dalian Univ Technol State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

Contact detection significantly affects the computational efficiency of discrete element simulations, especially for irregularly shaped elements. The dilated polyhedron is constructed by the Minkowski sum of a dilated sphere and a core convex polyhedron. One of the greatest advantages of using the dilated polyhedron in contact detection lies in its ability to be solved by calculating the nearest distance between corresponding core polyhedra. The approximate envelope function (AEF) of a dilated polyhedron is formed by the weighted summation of the second-order dilated function of the polyhedral and spherical functions. The AEF can be used to represent the element in the optimization model for the contact center. Geometric calculations are then employed for the contact points on the core polyhedron, whereupon the contact detection is solved. The accuracy and stability of the proposed method by a 3-D Voronoi tessellation are validated using analytical solutions and previously published simulation results. The efficiency tests show that the speedup of the CPU-based multithread algorithm can reach 14 on a desktop. The direct shear test of the Voronoi shaped ballast is analyzed by this method. The shear stress under different vertical pressure is compared with previously published experimental and simulated results.

关键词： contact detection dilated polyhedron direct shear test discrete element method potential function

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Isotopically invariant Dunham parameters and the potential function of the HCl molecule

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OPTICS AND SPECTROSCOPY 2002年第6期92卷 871-876页

作者： Velichko, TI Mikhailenko, SN Architectural & Construct Acad Tyumen 625000 Russia Russian Acad Sci Inst Atmospher Opt Siberian Div Tomsk 634055 Russia

The isotopically invariant Dunham parameters U-mj, Delta(mj)(H) and Delta(mj)(Cl) were determined by simultaneously fitting the line centers of vibration-rotation transitions of six isotopic HCl forms in the ground electronic state. Fitting included relations between U-mj values. The parameters of the isotopically invariant potential of HCl were determined using independent U-m0 and U-m1 values. The contributions to the vibrational terms of (HCl)-Cl-35 caused by violation of the Born-Oppenheimer approximation were calculated. (C) 2002 MAIK "Nauka/Interperiodica".

关键词： hydrochloric acid molecules Born-Oppenheimer approximation parameters MACHINE SHOP PRACTICE Invariant potential function vibration-rotation

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Lyapunov function as potential function: A dynamical equivalence

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Chinese Physics B 2014年第1期23卷 136-141页

作者：袁若石马易安苑波敖平 School of Biomedical Engineering Shanghai Jiao Tong University Shanghai Center for Systems Biomedicine Shanghai Jiao Tong University Department of Applied Mathematics University of Washington Department of Computer Science and Engineering Shanghai Jiao Tong University Department of Physics Shanghai Jiao Tong University

For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.

关键词： Lyapunov function potential function stochastic process generalized Einstein relation

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A quantum dynamics study of H₂+OH→H₂O+H employing the Wu-Schatz-Lendvay-Fang-Harding potential function and a four-atom implementation of the real wave packet method

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JOURNAL OF CHEMICAL PHYSICS 2002年第4期117卷 1604-1613页

作者： Goldfield, EM Gray, SK Wayne State Univ Dept Chem Detroit MI 48202 USA Argonne Natl Lab Div Chem Argonne IL 60439 USA

We carry out numerous six-dimensional wave packet propagations for H-2+OH-->H2O+H on the ab initio based, Wu-Schatz-Lendvay-Fang-Harding potential energy function. For comparison, some calculations are also carried out on the older but more widely studied potential function of Walch, Dunning, Schatz, and Elgersma. The energy dependence of the total angular momentum J=0 cumulative reaction probability is obtained and J-shifting is used to estimate the bimolecular rate constant as a function of temperature. Some J>0 calculations are also carried out. A novel J-shifting procedure, designed to more accurately describe the effects of angular momentum, is introduced. We compare our results with transition state theory calculations and experiment. An important feature of our work is the development of an efficient, four-atom, parallel implementation of the real wave packet method, augmented with a recently developed finite difference method. (C) 2002 American Institute of Physics.

关键词： Packet Real number Transition state theory RATE CONSTANT potential function Hydrogen Wave packets Finite difference methods hydroxyl ion

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