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Relaxed matching for stabilization of relative equilibria of mechanical systems

David Long, Dmitry V. Zenkov
2007 2007 46th IEEE Conference on Decision and Control  
The method of controlled Lagrangians is a technique for stabilizing relative equilibria of mechanical systems with symmetry.  ...  This paper develops a modification of kinetic shaping technique in the theory of controlled Lagrangians.  ...  The paper is organized as follows: In Section 2 we review the method of controlled Lagrangians for stabilization of relative equilibria of mechanical systems.  ... 
doi:10.1109/cdc.2007.4434506 dblp:conf/cdc/LongZ07 fatcat:twjrvpjrnfdk5obzxkvl5q3k4q

Flat nonholonomic matching

D.V. Zenkov, A.M. Bloch, J.E. Marsden
2002 Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)  
In this paper we extend the matching technique to a class of nonholonomic systems with symmetries.  ...  The method of controlled Lagrangians is then applied to these systems resulting in a smooth stabilizing controller.  ...  In [4] [5] [6] [7] the technique of controlled Lagrangians is developed for stabilization of relative equilibria of mechanical systems with cyclic symmetries.  ... 
doi:10.1109/acc.2002.1025215 fatcat:vrktrwjksvdjjn2zceqf4co7gy

Hopf Bifurcations in Coronal Loops. II. Nonlinear Evolution of Instabilities

D. Gomez, A. Sicardi Schifino, C. Ferro Fontan
1990 Astrophysical Journal  
The nonthermal Doppler widths of EUV lines forming in the transition region can be explained by the existence of relatively low amplitude limit cycles.  ...  We also show that this model can provide a natural explanation for the excess widths of EUV spectral lines formed in the transition region.  ...  It is important to note the quite slow relaxation time of the system for control parameter values sufficiently close to the critical point.  ... 
doi:10.1086/168539 fatcat:pm3qrhbm5becfgjviwnxehteiq

Topology trivialization transition in random non-gradient autonomous ODEs on a sphere

Y V Fyodorov
2016 Journal of Statistical Mechanics: Theory and Experiment  
We calculate the mean total number of equilibrium points in a system of N random autonomous ODE's introduced by Cugliandolo et al. in 1997 to describe non-relaxational glassy dynamics on the high-dimensional  ...  Classifying the equilibria in the nontrivial phase by stability remains an open problem.  ...  system of ODE's (1.2) is not-relaxational.  ... 
doi:10.1088/1742-5468/aa511a fatcat:hdqjbsqgzngzti2ybq7aegqs6a

Dynamical persistence in high-diversity resource-consumer communities

Itay Dalmedigos, Guy Bunin, James O'Dwyer
2020 PLoS Computational Biology  
When this ratio is smaller than one, dynamics will reach stable equilibria.  ...  If they are unstable, the system is repelled from fixed points, and abundances forever fluctuate.  ...  Biroli for helpful discussions. Author Contributions Conceptualization: Itay Dalmedigos, Guy Bunin. Investigation: Itay Dalmedigos, Guy Bunin.  ... 
doi:10.1371/journal.pcbi.1008189 pmid:33044951 fatcat:o6nuh7urlvgphcign42uzkinle

Stable Synchronization of Mechanical System Networks

Sujit Nair, Naomi Ehrich Leonard
2008 SIAM Journal of Control and Optimization  
In this paper we address stabilization of a network of underactuated mechanical systems with unstable dynamics.  ...  to couple the mechanical systems.  ...  Asymptotic Stabilization of Relative Equilibria.  ... 
doi:10.1137/050646639 fatcat:tm7lro4pbnhvzmghyuocad5hvy

Lie group variational integrators for the full body problem

Taeyoung Lee, Melvin Leok, N. Harris McClamroch
2007 Computer Methods in Applied Mechanics and Engineering  
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria of discrete mechanical systems with symmetry and equilibria of discrete mechanical systems with  ...  Controlled Lagrangian and matching techniques are developed for the stabilization of equilibria of discrete mechanical systems with symmetry as well as broken symmetry.  ... 
doi:10.1016/j.cma.2007.01.017 fatcat:4gasexilivapdnjg2egh6gbglq

Remarks on the relaxation approximation of the Burnett equations

Shi Jin, Marshall Slemrod
2001 Methods and Applications of Analysis  
As an illustrative example for this relaxation procedure, consider the following model problem (1.1) ut + uu x = eq x , (1-2) qt = -^, where e > 0.  ...  The purpose of this note is to present a short discussion of the relaxation regularization of the Burnett equations, a second order approximation via the Chapman-Enskog expansion on the Boltzmann equation  ...  Specifically if truncation of the Chapman-Enskog expansion beyond Navier-Stokes order leads to unphysical stability results perhaps system (1.1)-(1.2) which has stable equilibria and is well posed is indeed  ... 
doi:10.4310/maa.2001.v8.n4.a3 fatcat:4zwubzwvgfgr3a7olfi7xpar6a

Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances

Romeo Ortega, Jose Guadalupe Romero
2012 Systems & control letters (Print)  
For a class of fully actuated mechanical systems, a globally asymptotically stabilizing solution is given.  ...  Also, IC of passive systems rejects constant input disturbances, but no similar property can be ensured if the disturbance is not matched.  ...  Acknowledgements The authors thank Arjan van der Schaft and Alejandro Donaire for useful discussions, and Mickael Hilairet for bringing the interesting paper [4] to their attention.  ... 
doi:10.1016/j.sysconle.2011.09.015 fatcat:nyeqesrlybg63j4jpimr4ij7cy

Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances

Romeo Ortega, Jose Guadalupe Romero
2011 IEEE Conference on Decision and Control and European Control Conference  
For a class of fully actuated mechanical systems, a globally asymptotically stabilizing solution is given.  ...  Also, IC of passive systems rejects constant input disturbances, but no similar property can be ensured if the disturbance is not matched.  ...  Acknowledgements The authors thank Arjan van der Schaft and Alejandro Donaire for useful discussions, and Mickael Hilairet for bringing the interesting paper [4] to their attention.  ... 
doi:10.1109/cdc.2011.6160543 dblp:conf/cdc/OrtegaR11 fatcat:lxt5bwllbvgdrpuj4ks6xt7nwq

On the equilibrium morphology of systems drawn from spherical collapse experiments

C. M. Boily, E. Athanassoula
2006 Monthly notices of the Royal Astronomical Society  
We interpret this in terms of less-effective violent relaxation for more peaked profiles when more phase mixing takes place at the centre.  ...  We present a purely theoretical study of the morphological evolution of self-gravitating systems formed through the dissipationless collapse of N-point sources.  ...  Bosma for useful and motivating discussions and Jean-Charles Lambert for his invaluable help with the simulation software and the administration of the runs.  ... 
doi:10.1111/j.1365-2966.2006.10365.x fatcat:dnujiln44zfflk7cepvqk2lshm

Equilibrium selection and the dynamic evolution of preferences

Thomas W.L. Norman
2012 Games and Economic Behavior  
Moreover, a strong form of stability is established for the efficient outcome of games with common interests, whilst weaker stability results are provided for nonstrict efficient equilibria (including  ...  mixed-strategy equilibria) of doubly symmetric games.  ...  combination of payoff functions, the global payoff game delivers a simple, well-functioning dynamical system for the indirect evolution of those payoffs. 17 The Nash equilibria of G φ will, of course  ... 
doi:10.1016/j.geb.2011.05.005 fatcat:5vijajeqtbbhxfyifwwbifb6h4

Keystone Predation and Plant Species Coexistence: The Role of Carnivore Hunting Mode

V. Calcagno, C. Sun, O. J. Schmitz, M. Loreau
2011 American Naturalist  
These results extend our understanding of carnivore indirect effects in food webs and show that behavioral effects can have major consequences on plant community structure, stressing the need for theoretical  ...  Plant communities are shaped by bottom-up processes such as competition for nutrients and top-down processes such as herbivory.  ...  Leroux for helping improve the manuscript.  ... 
doi:10.1086/657436 pmid:21091211 fatcat:qndbl7c37behxccgz4s2fhasje

SLOW RISE AND PARTIAL ERUPTION OF A DOUBLE-DECKER FILAMENT. II. A DOUBLE FLUX ROPE MODEL

Bernhard Kliem, Tibor Török, Viacheslav S. Titov, Roberto Lionello, Jon A. Linker, Rui Liu, Chang Liu, Haimin Wang
2014 Astrophysical Journal  
Force-free equilibria containing two vertically arranged magnetic flux ropes of like chirality and current direction are considered as a model for split filaments/prominences and filament-sigmoid systems  ...  If this component decreases sufficiently, then both flux ropes turn unstable for conditions typical of solar active regions, with the lower rope typically being unstable first.  ...  B.K. acknowledges support by the DFG, the STFC, the NSF (grant AGS-1249270) and by the Chinese Academy of Sciences under grant 2012T1J0017. The contributions of T.T., V.S.T., R.  ... 
doi:10.1088/0004-637x/792/2/107 fatcat:64d3mozt2vghzj3l3t2tu4resu

Regional concentration of entrepreneurial activities

Graciela Kuechle
2014 Journal of Economic Behavior and Organization  
Although conspicuous examples point at the presence of positive feedback mechanisms, agglomerations also occur in the absence of these features and in areas of considerably homogeneous economic potential  ...  Strategic complementarities, knowledge spillovers and network externalities are regarded as the principal sources of such phenomena.  ...  Agglomerations and the Efficiency of the Global System We have characterized the situations leading to multiple equilibria and their stability and showed that persistent regional divergence can occur in  ... 
doi:10.1016/j.jebo.2014.03.017 fatcat:tcc5yttr6ber3mwf7757zyan5i
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