Готові списки джерел за темами / LAGRANGE MULTIPLIER TECHNIQUE

Добірка наукової літератури з теми "LAGRANGE MULTIPLIER TECHNIQUE"

Автор: Grafiati

Опубліковано: 11 вересня 2023

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Статті в журналах з теми "LAGRANGE MULTIPLIER TECHNIQUE"

Galanin, M. P., V. V. Lukin, and P. V. Solomentseva. "Comparison of the Lagrange Multipliers Function Approximation Methods in Solving Contact Problems by the Independent Contact Boundary Technique." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 6 (105) (December 2022): 17–32. http://dx.doi.org/10.18698/1812-3368-2022-6-17-32.

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The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies

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Matei, Andaluzia Cristina. "A Three-Field Variational Formulation for a Frictional Contact Problem with Prescribed Normal Stress." Fractal and Fractional 6, no. 11 (November 4, 2022): 651. http://dx.doi.org/10.3390/fractalfract6110651.

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In the present work, we address a nonlinear boundary value problem that models frictional contact with prescribed normal stress between a deformable body and a foundation. The body is nonlinearly elastic, the constitutive law being a subdifferential inclusion. We deliver a three-field variational formulation by means of a new variational approach governed by the theory of bipotentials combined with a Lagrange-multipliers technique. In this new approach, the unknown of the mechanical model is a triple consisting of the displacement field, a Lagrange multiplier related to the friction force and the Cauchy stress tensor. We obtain existence, uniqueness, boundedness and convergence results.

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Hu, Yun, and Qianqian Duan. "Solving the TSP by the AALHNN algorithm." Mathematical Biosciences and Engineering 19, no. 4 (2022): 3427–48. http://dx.doi.org/10.3934/mbe.2022158.

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<abstract> <p>It is prone to get stuck in a local minimum when solving the Traveling Salesman Problem (TSP) by the traditional Hopfield neural network (HNN) and hard to converge to an efficient solution, resulting from the defect of the penalty method used by the HNN. In order to mend this defect, an accelerated augmented Lagrangian Hopfield neural network (AALHNN) algorithm was proposed in this paper. This algorithm gets out of the dilemma of penalty method by Lagrangian multiplier method, ensuring that the solution to the TSP is undoubtedly efficient. The second order factor added in the algorithm stabilizes the neural network dynamic model of the problem, thus improving the efficiency of solution. In this paper, when solving the TSP by AALHNN, some changes were made to the TSP models of Hopfield and Tank. Say, constraints of TSP are multiplied by Lagrange multipliers and augmented Lagrange multipliers respectively, The augmented Lagrange function composed of path length function can ensure robust convergence and escape from the local minimum trap. The Lagrange multipliers are updated by using nesterov acceleration technique. In addition, it was theoretically proved that the extremum obtained by this improved algorithm is the optimal solution of the initial problem and the approximate optimal solution of the TSP was successfully obtained several times in the simulation experiment. Compared with the traditional HNN, this method can ensure that it is effective for TSP solution and the solution to the TSP obtained is better.</p> </abstract>

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Vyasarayani, C. P., Sukhpreet Singh Sandhu, and John McPhee. "Nonsmooth Modeling of Vibro-Impacting Euler-Bernoulli Beam." Advances in Acoustics and Vibration 2012 (September 12, 2012): 1–9. http://dx.doi.org/10.1155/2012/268595.

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A new technique to simulate nonsmooth motions occurring in vibro-impacting continuous systems is proposed. Sticking motions that are encountered during vibro-impact simulation are imposed exactly using a Lagrange multiplier, which represents the normal reaction force between the continuous system and the obstacle. The expression for the Lagrange multiplier is developed in closed form. The developed theory is demonstrated by numerically simulating the forced response of a pinned-pinned beam impacting a point-like rigid obstacle.

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Rodrigo, E., S. Tapia, J. M. Mera, and M. Soler. "Optimizing Electric Rail Energy Consumption Using the Lagrange Multiplier Technique." Journal of Transportation Engineering 139, no. 3 (March 2013): 321–29. http://dx.doi.org/10.1061/(asce)te.1943-5436.0000483.

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Sk, Nayem, and Abhik Kumar Sanyal. "On the equivalence between different canonical forms of F(R) theory of gravity." International Journal of Modern Physics D 27, no. 08 (May 30, 2018): 1850085. http://dx.doi.org/10.1142/s0218271818500852.

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Classical equivalence between Jordan’s and Einstein’s frame counterparts of [Formula: see text] theory of gravity has recently been questioned, since the two produce different Noether symmetries, which could not be translated back and forth using transformation relations. Here we add the Hamiltonian constraint equation, which is essentially the time–time component of Einstein’s equation, through a Lagrange multiplier to the existence condition for Noether symmetry and show that all the three different canonical structures of [Formula: see text] theory of gravity, including the one which follows from Lagrange multiplier technique, admit each and every available symmetry independently. This establishes classical equivalence.

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KHAN, NAWAB, QAZI MAHMOOD UL HASSAN, EHSAN UL HAQ, M. YAQUB KHAN, KAMRAN AYUB, and JAVERIYA AYUB. "ANALYTICAL TECHNIQUE WITH LAGRANGE MULTIPLIER FOR SOLVING SPECIFIC NONLINEAR DIFFERENTIAL EQUATIONS." Journal of Science and Arts 21, no. 1 (March 30, 2021): 5–14. http://dx.doi.org/10.46939/j.sci.arts-21.1-a01.

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This paper will use Lagrange parameter in Adomain decomposition method to suggest new method for solving nonlinear differential equation. This method will be highly order convergent. Also, this method will be compared with old existence method. At last, some numerical examples will be given to illustrate the efficiency of newly developed method.

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Negulescu, Claudia. "Mathematical Study of a Lagrange-Multiplier Technique for Stiff Transport Problems." Multiscale Modeling & Simulation 19, no. 2 (January 2021): 802–29. http://dx.doi.org/10.1137/20m1333717.

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Kuo, Way, Hsin-Hui Lin, Zhongkai Xu, and Weixing Zhang. "Reliability Optimization with the Lagrange-Multiplier and Branch-and-Bound Technique." IEEE Transactions on Reliability R-36, no. 5 (December 1987): 624–30. http://dx.doi.org/10.1109/tr.1987.5222487.

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Kanarska, Y., I. Lomov, and T. Antoun. "Mesoscale simulations of particulate flows with parallel distributed Lagrange multiplier technique." Computers & Fluids 48, no. 1 (September 2011): 16–29. http://dx.doi.org/10.1016/j.compfluid.2011.03.010.

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Дисертації з теми "LAGRANGE MULTIPLIER TECHNIQUE"

Gagnon, Michael Anthony. "An adaptive mixed finite element method using the Lagrange multiplier technique." Worcester, Mass. : Worcester Polytechnic Institute, 2009. http://www.wpi.edu/Pubs/ETD/Available/etd-050409-115850/.

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Анотація:

Thesis (M.S.)--Worcester Polytechnic Institute.
Keywords: a posteriori error estimate; adaptive; mesh refinement; lagrange multiplier; finite element method. Includes bibliographical references (leaf 26).

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Veeraklaew, Tawiwat. "Optimization of linear time-invariant dynamic systems without lagrange multipliers." Ohio University / OhioLINK, 1995. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1178821882.

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KAUSHIK, NIKITA, and KIRTI RANI. "NUMERICAL METHOD FOR SOLVING SINGULAR PERTURBED PROBLEM." Thesis, 2021. http://dspace.dtu.ac.in:8080/jspui/handle/repository/19014.

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Mathematical equations are used to model a variety of phenomena in natural sciences and engineering. Various parameters are included in these mathematical equations. The solutions of these equations are affected by minor changes in these parame ters. This minor alteration is called perturbation and the corresponding parameter is known as the perturbation parameter. It is difficult to find the exact solutions of these mathematical equations. Therefore, the alternative way is to find their approximate solutions. These solutions are ob tained by using the approximation techniques. These Perturbation techniques further pave the way to Perturbation theory. We begin with perturbation theory in chemical kinetics. With the introduction of Michaelis-Menten mechanism and steady state approximation the concept of singular perturbation theory in chemical kinetics is studied. As we move further, we discuss a weakly coupled system of m-equations and study a highly significant numerical method i.e. q-stage runge Kutta method. We then discuss a number of iterative methods to solve initial- and/or boundary-value problems in ordinary and partial differential equations. As a series of iterates, these iterative procedures have the solution or a close approximation to it. We present and evaluate an iterative analytic approach based on the Lagrange multiplier technique to estimate the multiscale solution. Iteration is used to achieve closed-form analytic approximations to nonlinear bound ary value problems. In a general setting, variational theory and Liouville–Green transforms are used to obtain the Lagrange multiplier optimally. We have taken singular peturbed problem to test the method and also compare it with the exact so lution. Further, two test partial differential equations problems are taken into account and the findings of a detailed comparative study are discussed.

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安田, 仁彦, 建瑞叶 та 恵輔神谷. "回転軸系の時間領域実験的同定法の開発とその応用に関する研究". 2000. http://hdl.handle.net/2237/12876.

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Книги з теми "LAGRANGE MULTIPLIER TECHNIQUE"

United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. Technique to eliminate computational instability in multibody simulations employing the Lagrange multiplier. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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National Aeronautics and Space Administration (NASA) Staff. Technique to Eliminate Computational Instability in Multibody Simulations Employing the Lagrange Multiplier. Independently Published, 2018.

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Частини книг з теми "LAGRANGE MULTIPLIER TECHNIQUE"

Li, Zi Cai. "Lagrange Multipliers and Other Coupling Techniques." In Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities, 209–24. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4613-3338-8_6.

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Chow, Gregory C. "Computation of Optimum Control Functions by Lagrange Multipliers." In Computational Techniques for Econometrics and Economic Analysis, 65–72. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8372-5_4.

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Fox, William P. "Constrained Nonlinear Optimization in Information Science." In Encyclopedia of Information Science and Technology, Fourth Edition, 4594–606. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-2255-3.ch399.

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Анотація:

This chapter provides an overview of constrained optimization methods. Background, theory, and examples are provided. Coverage includes Lagrange multipliers for equality constrained optimization with a Cobb-Douglass example from Information Science. We also provide Karush-Kuhn-Tucker for inequality constrained optimization and a production example for smart phones with inequalities. An overview and discussion of numerical methods and techniques is also provided. We also provide a brief list of technology available to assist in solving these constrained nonlinear optimization problems.

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Fox, William P. "Constrained Nonlinear Optimization in Information Science." In Advanced Methodologies and Technologies in Artificial Intelligence, Computer Simulation, and Human-Computer Interaction, 705–21. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-7368-5.ch053.

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Анотація:

This chapter provides an overview of constrained optimization methods. Background, theory, and examples are provided. Coverage includes Lagrange multipliers for equality constrained optimization with a Cobb-Douglass example from information science. The authors also provide Karush-Kuhn-Tucker for inequality-constrained optimization and a production example for smart phones with inequalities. An overview and discussion of numerical methods and techniques is also provided. The authors also provide a brief list of technology available to assist in solving these constrained nonlinear optimization problems.

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Тези доповідей конференцій з теми "LAGRANGE MULTIPLIER TECHNIQUE"

Cordina, Mario, and Carl J. Debono. "An adaptive Lagrange multiplier technique for multi-view video plus depth coding." In 2013 Picture Coding Symposium (PCS). IEEE, 2013. http://dx.doi.org/10.1109/pcs.2013.6737730.

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Grajek and Stankowski. "Rate-Distortion Optimized Quantization in Motion JPEG." In WSCG'2022 - 30. International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision'2022. Západočeská univerzita, 2022. http://dx.doi.org/10.24132/csrn.3201.29.

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Rate-Distortion Optimized Quantization (RDOQ) is an encoding optimization technique that may be applied to any transform-based compression technique preserving bitstream compliance with the standard. In the paper, the application of the RDOQ to Motion JPEG is described and evaluated. The proposed solution includes block- level optimization with picture-level Lagrange multiplier estimation. Performed evaluation results in higher compression ratios as compared to typical Motion JPEG.

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Hara, Kensuke, and Masahiro Watanabe. "Formulation of the Aeroelastic Instability Problem of Rectangular Plates in Uniform Flow Based on the Hamiltonian Mechanics for the Constrained System." In ASME 2014 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/pvp2014-28646.

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This paper addresses a formulation and an aeroelastic instability analysis of a plate in a uniform incompressible and irrotational flow based on the classical variational principle framework. Because of an intrinsic algebraic relation between the plate displacement and the velocity potential, this system has to be formulated as the constrained system. In this study, we tried to apply the Hamiltonian mechanics to the formulation of the fluid-structure interaction problem with mixed boundary condition. As a result, we obtain the canonical equations, that consist of the evolution equations for the plate displacement, the velocity potential, the Lagrange multiplier and canonically conjugate momenta for those physical quantities. In particular, it was found that the Lagrange multiplier was just the pressure. In other words, the equations of time evolution could be derived for not only the plate displacement and the velocity potential but also the pressure (the Lagrange multiplier). The stability of this system was analyzed by the eigenvalue analysis. Then, flutter modes, their frequencies and growth rates were discussed. The proposed technique has the advantage that it can reduce iteration procedures in the stability analysis. As a consequence, it can be expected that the stability of this system can be evaluated efficiently. This paper introduces a formulation of the only two dimensional problem, and the stability analysis of a clamped-free plate is implemented as an numerical example. Howerver, this formulation can be applied to three dimensional problems without intrinsic difficulties.

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Janjua, M., S. Nudurupati, P. Singh, I. Fischer, and Nadine Aubry. "Direct Numerical Simulation (DNS) of Suspensions in Spatially Varying Electric Fields." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-44094.

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We have developed a numerical scheme to simulate the motion of dielectric particles in uniform and nonuniform electric fields. The particles are moved using a direct simulation scheme in which the fundamental equations of motion of fluid and solid particles are solved without the use of models. The motion of particles is tracked using a distributed Lagrange multiplier method (DLM) and the electric force acting on the particles is calculated by integrating the Maxwell stress tensor (MST) over the particle surfaces. One of the key features of the DLM method is that the fluid-particle system is treated implicitly by using a combined weak formulation where the forces and moments between the particles and fluid cancel, as they are internal to the combined system. The flow inside the particles is forced to be a rigid-body motion using the distributed Lagrange multiplier method. The MST is obtained from the electric potential, which, in turn, is obtained by solving the electrostatic problem. In our numerical scheme the Marchuk-Yanenko operator-splitting technique is used to decouple the difficulties associated with the incompressibility constraint, the nonlinear convection term, and the rigid-body motion constraint. A comparison of the DNS results with those from the point-dipole approximation shows that the accuracy of the latter diminishes when the distance between the particles becomes comparable to the particle diameter, the domain size is comparable to the diameter, and also when the dielectric mismatch between the fluid and particles is relatively large.

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Ganovski, Latchezar L., Paul Fisette, and Jean-Claude Samin. "Modeling of Overactuated Closed-Loop Mechanisms With Singularities: Simulation and Control." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21324.

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Abstract The modeling and control of redundantly actuated closed-loop mechanical systems is considered in the present work an illustrated with a planar four-bar mechanism and a 3-D parallel manipulator. A specific trajectory involving singular configurations is generated and then followed using the overactuation. To generate the trajectory, four-degree polynomial functions are considered. The loop constraint equations are solved by means of the Newton-Raphson numerical algorithm. In order to describe the dynamics of the systems, the Lagrange multiplier technique is used. The multipliers are eliminated via the coordinate partitioning method. To overcome the underdetermined state of the system induced by the overactuation, additional equations that represent a specific condition for smoothly passing through the singularities are applied. Further, to control the redundantly actuated mechanisms a feed-forward controller is chosen. The robustness of the controller is investigated through several cases of simulation including random noise applied to the controller input and instantaneous loading.

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Potter, T. E., K. D. Willmert, and M. Sathyamoorthy. "Nonlinear Optimal Design of Dynamic Mechanical Systems." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0350.

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Abstract Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraints and revises the Gauss nonlinearly constrained method for quadratic constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that when the iteration process terminates, these conditions are automatically satisfied. Although the technique was developed for mechanism problems, it is applicable to any optimization problem having the form of a sum of squares objective function subjected to nonlinear constraints.

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Tangpong, X. W., and Om P. Agrawal. "Fractional Optimal Control of Distributed Systems." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43046.

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This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a Fractional Optimal Control Problem (FOCP) is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE). The scheme presented rely on reducing the equations for distributed system into a set of equations that have no space parameter. Several strategies are pointed out for this task, and one of them is discussed in detail. This involves discretizing the space domain into several segments, and writing the spatial derivatives in terms of variables at space node points. The Calculus of Variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler-Lagrange equations for the problem. The numerical technique presented in [1] for scalar case is extended for the vector case. In this technique, the FOC equations are reduced to Volterra type integral equations. The time domain is also descretized into several segments. For the linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for various order of fractional derivatives and various order of space and time discretizations. Numerical results show that for the problem considered, only a few space grid points are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced. The formulation presented is simple and can be extended to FOC of other distributed systems.

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Agrawal, Om P. "Fractional Optimal Control of a Distributed System Using Eigenfunctions." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35921.

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This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equations (PFDEs). Eigenfunctions are used to eliminate the space parameter, and to define the problem in terms of a set of state and control variables. This leads to a multi FOCP in which each FOCP could be solved independently. Several other strategies are pointed out to reduce the problem to a finite dimensional space, some of which may not provide a decoupled set of equations. The Calculus of Variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler-Lagrange equations for the problem. The numerical technique presented in [1] is used to obtain the state and the control variables. In this technique, the FOC equations are reduced to Volterra type integral equations. The time domain is descretized into several segments and a time marching scheme is used to obtain the response at discrete time points. For a linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for different number of eigenfunctions and time discretizations. Numerical results show that only a few eigenfunctions are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced. The formulation presented is simple and can be extended to FOC of other distributed systems.

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Nikravesh, P. E., and G. Gim. "Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loops." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0102.

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Abstract This paper presents a systematic method for deriving the minimum number of equations of motion for multibody system containing closed kinematic loops. A set of joint or natural coordinates is used to describe the configuration of the system. The constraint equations associated with the closed kinematic loops are found systematically in terms of the joint coordinates. These constraints and their corresponding elements are constructed from known block matrices representing different kinematic joints. The Jacobian matrix associated with these constraints is further used to find a velocity transformation matrix. The equations of motions are initially written in terms of the dependent joint coordinates using the Lagrange multiplier technique. Then the velocity transformation matrix is used to derive a minimum number of equations of motion in terms of a set of independent joint coordinates. An illustrative example and numerical results are presented, and the advantages and disadvantages of the method are discussed.

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Kadaksham, J., J. Batton, P. Singh, and N. Aubry. "Micro Fluidic Platform for Manipulation of Micro- and Nanoscale Particles." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41582.

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In this paper, we study the manipulation and immobilization of micro- and nano-sized particles, such as living cells, suspended in a liquid. Our technique focuses on dielectrophoresis, that is, the use of spatially nonuniform electric field, while not damaging the manipulated particles or cells. The small size of the particles considered here requires the use of micro-electro-mechanical device (MEMS). We first simulate the suspended system by means of our new computational fluid dynamics (CFD) tool based on the distributed Lagrange Multiplier method (DLM), which takes into account not only fluid-particle but also particle-particle interactions. Results for both positive and negative dielectrophoresis are presented. We also show the existence of various regimes for the particle structures depending on the relative magnitude of the dielectrophoretic force and the electrostatic particle-particle interactions. We then design, fabricate and test a MEMS platform containing several microdevices.

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