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Journal articles on the topic 'Système Lagrangien'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 February 2022

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1

Cresson, Jacky, and Sébastien Darses. "Plongement stochastique des systèmes lagrangiens." Comptes Rendus Mathematique 342, no. 5 (March 2006): 333–36. http://dx.doi.org/10.1016/j.crma.2005.12.028.

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2

Wang, Qing-Guo. "Identifiability of Lagrangian Systems With Application to Robot Manipulators." Journal of Dynamic Systems, Measurement, and Control 113, no. 2 (June 1, 1991): 289–94. http://dx.doi.org/10.1115/1.2896377.

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The deterministic parameter identifiability of mechanical linear and nonlinear dynamical systems is considered via linear parameterization of system Lagrangians and necessary and sufficient conditions are established on the identifiability for linear parameters. The identifiability condition results in a new concept, the irreducible Lagrangian representation, and it is introduced to characterize a system Lagrangian with the minimal number of identifiable parameters. A linear parameterization of the Lagrangians for n-degree-of-freedom robot manipulators with rotary joints is presented and, with the help of kinematic analysis, the irreducible representations are further obtained for the PUMA 560 and planar manipulators.
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3

Jumarie, Guy. "A New Class of P.I.D. Parameter Adaptation Algorithms for Robot Manipulators." Robotica 9, no. 1 (January 1991): 107–9. http://dx.doi.org/10.1017/s0263574700015629.

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SUMMARYBy using very simple considerations related to the mechanical Lagrangian itself, one obtains a new general class of parameter adaptation algorithms for robot manipulators, which provides such approaches as PID adaptation schemes. These models could apply to random structural mechanical Systems, subject to the conditon that they are defined by Lagrangians.
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4

Billionnet, A., and S. Elloumi. "Placement de tâches dans un système distribué et dualité lagrangienne." RAIRO - Operations Research 26, no. 1 (1992): 83–97. http://dx.doi.org/10.1051/ro/1992260100831.

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5

CHIERCHIA, LUIGI, and FABIO PUSATERI. "Analytic Lagrangian tori for the planetary many-body problem." Ergodic Theory and Dynamical Systems 29, no. 3 (June 2009): 849–73. http://dx.doi.org/10.1017/s0143385708000503.

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AbstractIn 2004, Féjoz [Démonstration du ‘théoréme d’Arnold’ sur la stabilité du système planétaire (d’après M. Herman). Ergod. Th. & Dynam. Sys.24(5) (2004), 1521–1582], completing investigations of Herman’s [Démonstration d’un théoréme de V.I. Arnold. Séminaire de Systémes Dynamiques et manuscripts, 1998], gave a complete proof of ‘Arnold’s Theorem’ [V. I. Arnol’d. Small denominators and problems of stability of motion in classical and celestial mechanics. Uspekhi Mat. Nauk. 18(6(114)) (1963), 91–192] on the planetary many-body problem, establishing, in particular, the existence of a positive measure set of smooth (C∞) Lagrangian invariant tori for the planetary many-body problem. Here, using Rüßmann’s 2001 KAM theory [H. Rüßmann. Invariant tori in non-degenerate nearly integrable Hamiltonian systems. R. & C. Dynamics2(6) (2001), 119–203], we prove the above result in the real-analytic class.
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6

Fathi, Albert. "Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 324, no. 9 (May 1997): 1043–46. http://dx.doi.org/10.1016/s0764-4442(97)87883-4.

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7

Krupková, Olga. "Noether theorem and first integrals of constrained Lagrangean systems." Mathematica Bohemica 122, no. 3 (1997): 257–65. http://dx.doi.org/10.21136/mb.1997.126152.

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8

Mason, Evan, Francois Colas, and Josep L. Pelegrí. "A Lagrangian study tracing water parcel origins in the Canary Upwelling System." Scientia Marina 76, S1 (August 31, 2012): 79–94. http://dx.doi.org/10.3989/scimar.03608.18d.

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9

Gay-Balmaz, François, and Hiroaki Yoshimura. "Dirac structures and variational formulation of port-Dirac systems in nonequilibrium thermodynamics." IMA Journal of Mathematical Control and Information 37, no. 4 (July 27, 2020): 1298–347. http://dx.doi.org/10.1093/imamci/dnaa015.

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Abstract The notion of implicit port-Lagrangian systems for nonholonomic mechanics was proposed in Yoshimura & Marsden (2006a, J. Geom. Phys., 57, 133–156; 2006b, J. Geom. Phys., 57, 209–250; 2006c, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto) as a Lagrangian analogue of implicit port-Hamiltonian systems. Such port-systems have an interconnection structure with ports through which power is exchanged with the exterior and which can be modeled by Dirac structures. In this paper, we present the notions of implicit port-Lagrangian systems and port-Dirac dynamical systems in nonequilibrium thermodynamics by generalizing the Dirac formulation to the case allowing irreversible processes, both for closed and open systems. Port-Dirac systems in nonequilibrium thermodynamics can be also deduced from a variational formulation of nonequilibrium thermodynamics for closed and open systems introduced in Gay-Balmaz & Yoshimura (2017a, J. Geom. Phys., 111, 169–193; 2018a, Entropy, 163, 1–26). This is a type of Lagrange–d’Alembert principle for the specific class of nonholonomic systems with nonlinear constraints of thermodynamic type, which are associated to the entropy production equation of the system. We illustrate our theory with some examples such as a cylinder-piston with ideal gas, an electric circuit with entropy production due to a resistor and an open piston with heat and matter exchange with the exterior.
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10

Tamminen, Eero V. "Strong Lagrange duality and the maximum principle for nonlinear discrete time optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 20. http://dx.doi.org/10.1051/cocv/2018012.

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We examine discrete-time optimal control problems with general, possibly non-linear or non-smooth dynamic equations, and state-control inequality and equality constraints. A new generalized convexity condition for the dynamics and constraints is defined, and it is proved that this property, together with a constraint qualification constitute sufficient conditions for the strong Lagrange duality result and saddle-point optimality conditions for the problem. The discrete maximum principle of Pontryagin is obtained in a straightforward manner from the strong Lagrange duality theorem, first in a new form in which the Lagrangian is minimized both with respect to the state and to the control variables. Assuming differentiability, the maximum principle is obtained in the usual form. It is shown that dynamic systems satisfying a global controllability condition with convex costs, have the required convexity property. This controllability condition is a natural extension of the customary directional convexity condition applied in the derivation of the discrete maximum principle for local optima in the literature.
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11

Jumarie, Guy. "Forces of reaction and neighbouring Hamilton's principle in the tracking control of manipulators via a sliding scheme." Robotica 11, no. 3 (May 1993): 227–32. http://dx.doi.org/10.1017/s026357470001609x.

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SUMMARYIt is shown that if one comes back to the formulation of the Hamilton's variational principle, it is then possible to obtain new viewpoints on the tracking control of robot manipulators. First, the Lagrange multiplier associated to the sliding surface can be interpretated in terms of control effort and/or forces of reaction of the mechanical system. Secondly, one can use the Taylor expansion of the mechanical Lagrangian, combined with a neighbour- ing Hamilton's principle, to obtain control schemes via sliding surfaces. Thirdly, a perturbation approach combined with the neighbouring Hamilton's principle provides results on the robustness of the control.
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12

Levant, Yves, and Marc Nikitin. "Can cost and financial accounting be fully re-integrated? The role of the French state in the separation of accounting systems and the failed attempt of the système croisé to re-integrate them." Accounting History 17, no. 3-4 (August 2012): 437–61. http://dx.doi.org/10.1177/1032373212443954.

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This article questions whether the separation of financial and cost accounting in France is an irreversible trend. We begin by showing that the integration of financial and cost accounting was quite “natural” up until the 1940s. We then show that after that date, State-imposed standardization of financial accounting led to separation of the two types of accounting. Last, we study the efforts of one individual, Jean-Pierre Lagrange, to promote a return to an integrated accounting system in the 1980s by means of his method named the système croisé. His efforts were in vain. In our opinion, this failure was not due to technical reasons, but can be attributed to the interaction of the interests of the main actors. Among these actors, the State played a dominant role in France by standardizing financial accounting. In addition, Lagrange was unable to obtain the backing of a network of allies to spread his accounting system.
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13

Barrios, Melani, and Gabriela Reyero. "An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives." Statistics, Optimization & Information Computing 8, no. 2 (May 18, 2020): 590–601. http://dx.doi.org/10.19139/soic-2310-5070-865.

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In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputofractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the basic and isoperimetric problems, one in an integral form, and the other that depends only on the Caputo derivatives. The advantage is that Caputo derivatives are more appropriate for modeling problems than the Riemann-Liouville derivatives and makes the calculations easier to solve because, in some cases, its behavior is similar to the behavior of classical derivatives. Finally, anew exact solution for a particular variational problem is obtained.
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14

Korkealaakso, Pasi, Asko Rouvinen, and Aki Mikkola. "Multibody Approach for Model-Based Fault Detection of a Reel." Journal of Computational and Nonlinear Dynamics 1, no. 2 (October 21, 2005): 116–22. http://dx.doi.org/10.1115/1.2162865.

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In order to improve the recognition of faulty situations, model-based fault detection can be used together with signal processing methods. In this study, faults and abnormalities of a reel are studied by employing the multibody simulation approach. The reel under consideration consists of a number of subsystems, including hydraulics, electrical drives, and mechanical parts. These subsystems are coupled by joints, friction forces, and contact forces. Using the multibody simulation approach, the complete model of the reel can be obtained by coupling different subsystems together. Three well-known multibody formulations, a method of Lagrange multipliers, an Augmented Lagrangian method, and a method based on projection matrix R, are briefly described and compared in order to find out the most efficient method for simulating the studied reel. Although this study is focused on the simulation of fault scenarios, the introduced multibody simulation approach can be utilized in real-time simulation. This makes it possible to apply the model to an existing reel.
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15

Després, Bruno. "Inégalité entropique pour un solveur conservatif du système de la dynamique des gaz en coordonnées de Lagrange." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 324, no. 11 (June 1997): 1301–6. http://dx.doi.org/10.1016/s0764-4442(99)80417-0.

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16

Damasceno, J. G., J. A. G. Miranda, and L. G. Perona. "A Note on Tonelli Lagrangian Systems on $\mathbb{T}^2$ with Positive Topological Entropy on a High Energy Level." Nelineinaya Dinamika 16, no. 4 (2020): 625–35. http://dx.doi.org/10.20537/nd200407.

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In this work we study the dynamical behavior of Tonelli Lagrangian systems defined on the tangent bundle of the torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$. We prove that the Lagrangian flow restricted to a high energy level $E_{L}^{-1}(c)$ (i.e., $c > c_0(L)$) has positive topological entropy if the flow satisfies the Kupka-Smale property in $E_{L}^{-1}(c)$ (i.e., all closed orbits with energy c are hyperbolic or elliptic and all heteroclinic intersections are transverse on $E_{L}^{-1}(c)$). The proof requires the use of well-known results from Aubry – Mather theory.
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17

Aguilar-Acevedo, Francisco, Ana Patricia Matus-Vicente, Miguel Ángel Hernández-López, J. Jesús Arellano-Pimente, Sergio Sánchez-Sánchez, and Daniel Pacheco-Bautist. "Modelado Euler-Lagrange del rotor de un aerogenerador tripala como sistema multicuerpo." Revista UIS Ingenierías 19, no. 1 (January 1, 2020): 25–36. http://dx.doi.org/10.18273/revuin.v19n1-2020002.

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Con el propósito de desarrollar estrategias para el mayor aprovechamiento del recurso eólico, es necesario disponer de modelos confiables para simular la respuesta de los aerogeneradores. Si bien, los fabricantes cuentan con modelos detallados, estos son generalmente de “caja negra”, lo que los hace incluso inutilizable en nuevos diseños. Así, los llamados modelos genéricos han proliferado. Bajo este enfoque, en este artículo se presenta el modelado dinámico del rotor de unaerogenerador tripala usando la formulación Euler-Lagrange. Para su análisis el rotor es descrito como un sistema multicuerpo de cuatro grados de libertad empleando matrices de transformación simplificadas. Se exponenlos detalles de la obtención del modelo, y la interpretación de su simulación tridimensional (3D) bajo diversas condiciones, que garantiza una fácil comprobación de la fiabilidad del modelo
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18

Farhan, Marwa K., and Muayad S. Croock. "Optimized routing algorithm for maximizing transmission rate in D2D network." Indonesian Journal of Electrical Engineering and Computer Science 23, no. 1 (June 1, 2021): 575. http://dx.doi.org/10.11591/ijeecs.v23.i1.pp575-582.

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<span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Wireless devices have been equiping extensive services over recent years. Since most of these devices are randomly distributed, a fundamental trade-off to be addressed is the transmission rate, latency, and packet loss of the ad hoc route selection in device to device (D2D) networks. Therefore, this paper introduces a notion of weighted transmission rate and total delay, as well as the probability of packet loss. By designing optimal transmission algorithms, this proposed algorithm aims to select the best path for device-to-device communication that maximizes the transmission rate while maintaining minimum delay and packet loss. Using the Lagrange optimization method, the lagrangian optimization of rate, delay, and the probability of packet loss algorithm (LORDP) is modeled. For practical designation, we consider the fading effect of the wireless channels scenario. The proposed optimal algorithm is modeled to compute the optimal cost objective function and represents the best possible solution for the corresponding path. Moreover, a simulation for the optimized algorithm is presented based on optimal cost objective function. Simulation results establish the efficiency of the proposed LORDP algorithm</span><span>.</span><span style="font-size: 9pt; font-family: 'Times New Roman', serif;">Wireless devices have been equiping extensive services over recent years. Since most of these devices are randomly distributed, a fundamental trade-off to be addressed is the transmission rate, latency, and packet loss of the ad hoc route selection in device to device (D2D) networks. Therefore, this paper introduces a notion of weighted transmission rate and total delay, as well as the probability of packet loss. By designing optimal transmission algorithms, this proposed algorithm aims to select the best path for device-to-device communication that maximizes the transmission rate while maintaining minimum delay and packet loss. Using the Lagrange optimization method, the lagrangian optimization of rate, delay, and the probability of packet loss algorithm (LORDP) is modeled. For practical designation, we consider the fading effect of the wireless channels scenario. The proposed optimal algorithm is modeled to compute the optimal cost objective function and represents the best possible solution for the corresponding path. Moreover, a simulation for the optimized algorithm is presented based on optimal cost objective function. Simulation results establish the efficiency of the proposed LORDP algorithm</span>
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19

Étienne, Jocelyn, and Pierre Saramito. "Estimations d'erreur a priori de la méthode de Lagrange–Galerkin pour les systèmes de type Kazhikhov–Smagulov." Comptes Rendus Mathematique 341, no. 12 (December 2005): 769–74. http://dx.doi.org/10.1016/j.crma.2005.10.005.

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20

Wang, Hanlei. "Towards manipulability of interactive Lagrangian systems." Automatica 119 (September 2020): 108913. http://dx.doi.org/10.1016/j.automatica.2020.108913.

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21

Meng, Ziyang, Tao Yang, Guodong Shi, Dimos V. Dimarogonas, Yiguang Hong, and Karl Henrik Johansson. "Targeted agreement of multiple Lagrangian systems." Automatica 84 (October 2017): 109–16. http://dx.doi.org/10.1016/j.automatica.2017.07.010.

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22

Layton, R. A., and B. C. Fabien. "Systematic Modelling Using Lagrangian DAEs." Mathematical and Computer Modelling of Dynamical Systems 7, no. 3 (September 1, 2001): 273–304. http://dx.doi.org/10.1076/mcmd.7.3.273.3642.

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23

Saha, Ananya, and Buddhadeb Sau. "Network localisation using Lagrangian optimisation." International Journal of Sensor Networks 31, no. 2 (2019): 65. http://dx.doi.org/10.1504/ijsnet.2019.10023448.

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24

Saha, Ananya, and Buddhadeb Sau. "Network localisation using Lagrangian optimisation." International Journal of Sensor Networks 31, no. 2 (2019): 65. http://dx.doi.org/10.1504/ijsnet.2019.102183.

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25

Hurtado, John E., and Andrew J. Sinclair. "Lagrangian mechanics of overparameterized systems." Nonlinear Dynamics 66, no. 1-2 (January 12, 2011): 201–12. http://dx.doi.org/10.1007/s11071-010-9921-1.

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26

Alvarez, Joaquin, David Rosas, Daniel Hernandez, and Ervin Alvarez. "Robust synchronization of arrays of Lagrangian systems." International Journal of Control, Automation and Systems 8, no. 5 (October 2010): 1039–47. http://dx.doi.org/10.1007/s12555-010-0513-0.

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27

Krzywiecki, Ł., M. Kutyłowski, and M. Nikodem. "General anonymous key broadcasting via Lagrangian interpolation." IET Information Security 2, no. 3 (2008): 79. http://dx.doi.org/10.1049/iet-ifs:20070122.

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28

Wang, Hongjun, Zhuoqun Zhao, and Tao Li. "Networked Euler-Lagrangian Systems Synchronization under Time-Varying Communicating Delays." Information 10, no. 1 (January 1, 2019): 14. http://dx.doi.org/10.3390/info10010014.

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This paper investigates the problem of the task-space synchronization control for networked Euler-Lagrange systems. In the considered systems, there are time-varying delays existing in the networking links and every subsystem contains uncertainties in both kinematics and dynamics. By adding new time-varying coupling gains, the negative effects caused by time-varying delays are eliminated. Moreover, to address the difficulties of parametric calibration, an adaptively synchronous protocol and adaptive laws are designed to online estimate kinematics and dynamic uncertainties. Through a Lyapunov candidate and a Lyapunov-Krasovskii functional, the asymptotic convergences of tracking errors and synchronous errors are rigorously proved. The simulation results demonstrate the proposed protocol guaranteeing the cooperative tracking control of the uncalibrated networked Euler-Lagrange systems in the existence of time-varying delays.
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29

Fahrenthold, E. P., and J. D. Wargo. "Lagrangian Bond Graphs for Solid Continuum Dynamics Modeling." Journal of Dynamic Systems, Measurement, and Control 116, no. 2 (June 1, 1994): 178–92. http://dx.doi.org/10.1115/1.2899209.

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The limitations of existing continuum bond graph modeling techniques have effectively precluded their use in large order problems, where nonrepetitive graph structures and causal patterns are normally present. As a result, despite extensive publication of bond graph models for continuous systems simulations, bond graph methods have not offered a viable alternative to finite element analysis for the vast majority of practical problems. However, a new modeling approach combining Lagrangian (mass fixed) bond graphs with a selected finite element discretization scheme allows for direct simulation of a wide range of large order solid continuum dynamics problems. With appropriate modifications, including the use of Eulerian (space fixed) bond graphs, the method may be extended to include fluid dynamics modeling.
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30

Zhang, Yan, and Michael M. Zavlanos. "Augmented Lagrangian optimization under fixed-point arithmetic." Automatica 122 (December 2020): 109218. http://dx.doi.org/10.1016/j.automatica.2020.109218.

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31

Goodwin, Graham C., José A. De Doná, María M. Seron, and Xiang W. Zhuo. "Lagrangian duality between constrained estimation and control." Automatica 41, no. 6 (June 2005): 935–44. http://dx.doi.org/10.1016/j.automatica.2004.12.014.

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32

Liu, Hanbing, and Gengsheng Wang. "Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 24. http://dx.doi.org/10.1051/cocv/2021028.

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In this paper, we study second-order optimality conditions for some optimal control problems governed by some semi-linear parabolic equations with periodic state constraint in time. We obtain a necessary condition and a sufficient condition in terms of the second order derivative of the associated Lagrangian. These two conditions correspond to the positive definite and the nonnegativity of the second order derivative of the Lagrangian on the same cone, respectively.
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33

Snyder, William, Christopher Roman, and Stephen Licht. "Complementary control allocation for a Lagrangian seafloor imaging platform." IFAC-PapersOnLine 49, no. 23 (2016): 465–69. http://dx.doi.org/10.1016/j.ifacol.2016.10.449.

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34

Maschke, Bernhard, and Arjan van der Schaft. "Linear Boundary Port Hamiltonian Systems defined on Lagrangian submanifolds." IFAC-PapersOnLine 53, no. 2 (2020): 7734–39. http://dx.doi.org/10.1016/j.ifacol.2020.12.1526.

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35

Dumitrescu, Sorina, and Xiaolin Wu. "Lagrangian Optimization of Two-Description Scalar Quantizers." IEEE Transactions on Information Theory 53, no. 11 (November 2007): 3990–4012. http://dx.doi.org/10.1109/tit.2007.907498.

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36

Kim, Yong-Hyuk, Yourim Yoon, and Byung-Ro Moon. "A Lagrangian Approach for Multiple Personalized Campaigns." IEEE Transactions on Knowledge and Data Engineering 20, no. 3 (2008): 383–96. http://dx.doi.org/10.1109/tkde.2007.190701.

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37

Hsieh, Fu-Shiung. "Combinatorial reverse auction based on revelation of Lagrangian multipliers." Decision Support Systems 48, no. 2 (January 2010): 323–30. http://dx.doi.org/10.1016/j.dss.2009.08.009.

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38

Cotsaftis, M., and C. Vibet. "Consistent impulse conditions in Lagrangian system dynamics." Robotica 6, no. 4 (October 1988): 339–41. http://dx.doi.org/10.1017/s0263574700004719.

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SUMMARYThe general problem of including impulse effects in Lagrangian dynamics is discussed. A self-consistent method is developed, and a block-diagram representation, including initial conditions, is introduced that displays the feature of the method. Example of a collision of two dissimilar robots is provided for illustration.
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39

Faye, Alain, and Frédéric Roupin. "Partial Lagrangian relaxation for general quadratic programming." 4OR 5, no. 1 (July 21, 2006): 75–88. http://dx.doi.org/10.1007/s10288-006-0011-7.

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40

Lee, H. "Parallel Lagrangean Approximation Procedure." Journal of the Operational Research Society 49, no. 11 (November 1998): 1164. http://dx.doi.org/10.2307/3010097.

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41

Lee, H. "Parallel Lagrangean approximation procedure." Journal of the Operational Research Society 49, no. 11 (November 1998): 1164–72. http://dx.doi.org/10.1057/palgrave.jors.2600629.

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42

BAHARIN, I. B., and R. J. GREEN. "Computationally-effective recursive lagrangian formulation of manipulation dynamics." International Journal of Control 54, no. 1 (July 1991): 195–214. http://dx.doi.org/10.1080/00207179108934156.

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43

Li, Chang-Jin. "A New Lagrangian Formulation of Dynamics for Robot Manipulators." Journal of Dynamic Systems, Measurement, and Control 111, no. 4 (December 1, 1989): 559–66. http://dx.doi.org/10.1115/1.3153092.

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In this paper, a new Lagrangian formulation of dynamics for robot manipulators is developed. The formulation results in well structured form equations of motion for robot manipulators. The equations are an explicit set of closed form second order highly nonlinear and coupling differential equations, which can be used for both the design of the control system (or dynamic simulation) and the computation of the joint generalized forces/torques. The mathematical operations of the formulation are so few that it is possible to realize the computation of the Lagrangian dynamics for robot manipulators in real-time on a micro/mini-computer. For a robot manipulator with n degrees-of-freedom, the number of operations of the formulation is at most (6n2 + 107n − 81) multiplications and (4n2 + 102n − 86) additions; for n = 6, about 780 multiplications and 670 additions.
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44

Alperin, Hernán, and Ivo Nowak. "Lagrangian Smoothing Heuristics for Max-Cut." Journal of Heuristics 11, no. 5-6 (December 2005): 447–63. http://dx.doi.org/10.1007/s10732-005-3603-z.

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45

Choi, Y. "PID state estimator for Lagrangian systems." IET Control Theory & Applications 1, no. 4 (July 1, 2007): 937–45. http://dx.doi.org/10.1049/iet-cta:20050512.

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46

Jouffroy, J., Q. Y. Zhou, and O. Zielinski. "n Active Current Selection for Lagrangian Profilers." Modeling, Identification and Control: A Norwegian Research Bulletin 34, no. 1 (2013): 1–10. http://dx.doi.org/10.4173/mic.2013.1.1.

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47

Tanonkou, G. A., L. Benyoucef, and Xiaolan Xie. "Design of Stochastic Distribution Networks Using Lagrangian Relaxation." IEEE Transactions on Automation Science and Engineering 5, no. 4 (October 2008): 597–608. http://dx.doi.org/10.1109/tase.2008.917156.

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48

Stanfel, L. E. "A recursive Lagrangian method for clustering problems." European Journal of Operational Research 27, no. 3 (December 1986): 332–42. http://dx.doi.org/10.1016/0377-2217(86)90330-9.

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49

Gu, Hanyu, Julia Memar, and Yakov Zinder. "Improved Lagrangian relaxation based optimization procedure for scheduling with storage." IFAC-PapersOnLine 52, no. 13 (2019): 100–105. http://dx.doi.org/10.1016/j.ifacol.2019.11.159.

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50

Sira-Ramirez, H., and Z. Gao. "Flatness based ADRC Control of Lagrangian Systems: A moving crane." IFAC-PapersOnLine 53, no. 2 (2020): 1337–42. http://dx.doi.org/10.1016/j.ifacol.2020.12.1870.

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