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Contraction Analysis of Nonlinear DAE Systems [article]

Hung D. Nguyen, Thanh Long Vu, Jean-Jacques Slotine, Konstantin Turitsyn
2017 arXiv   pre-print
This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems.  ...  We show that for a contracting DAE system, the reduced system always contracts faster than the extended ones; furthermore, there always exists an extension with contraction rate arbitrarily close to that  ...  ACKNOWLEDGMENT This work was supported in part by NSF-ECCS award ID 1508666, MIT/Skoltech and Masdar Initiative, Ministry of Education and Science of Russian Federation, Grant agreement No. 14.615.21.0001  ... 
arXiv:1702.07421v1 fatcat:fcbi4hjderbxtmjkugzt4tyiaq

A time integration algorithm for flexible mechanism dynamics: The DAE α-method

Jeng Yen, Linda Petzold, Soumyendu Raha
1998 Computer Methods in Applied Mechanics and Engineering  
Convergence and stability analysis is given and verifies that the DAE o-methods introduce no additional oscillations and preserve the stability of the underlying ODE system.  ...  Convergence of the Newton iteration, which can be a source of difficulty in solving nonlinear oscillatory systems with large stepsizes, is achieved via a coordinate-split modification to the Newton iteration  ...  cooperative agreement numbers DAAH04-95-2-0003 /contract number DDAH04-95-C-0008, and by AR0 contract number DAAH04-94-6-0208 and DAAH04-94-6-0213, the content of which does not necessarily reflect the  ... 
doi:10.1016/s0045-7825(97)00261-2 fatcat:p42kdmqjojcdheyel4pwaf5dy4

High-order Differentiable Autoencoder for Nonlinear Model Reduction [article]

Siyuan Shen, Yang Yin, Tianjia Shao, He Wang, Chenfanfu Jiang, Lei Lan, Kun Zhou
2021 arXiv   pre-print
Solving the nonlinear force equilibrium is even more challenging if the standard Newton's method is to be used.  ...  Along this pipeline, we also design a sampling network and a weighting network to enable weight-varying Cubature integration in order to incorporate nonlinearity in the model reduction.  ...  Most of them end up with solving a large-scale nonlinear system if an implicit time integration scheme is used.  ... 
arXiv:2102.11026v1 fatcat:biekm6nrvngrjdcligsgg7lsxi

Hybrid Analysis of Nonlinear Time-Varying Circuits Providing DAEs with Index at Most One [chapter]

Satoru Iwata, Mizuyo Takamatsu, Caren Tischendorf
2010 Mathematics in Industry  
However, it may lead to differential-algebraic equations (DAEs) with higher index. Here, we present a hybrid analysis for nonlinear time-varying circuits leading to DAEs with index at most one.  ...  Moreover, we prove that the minimum index of the DAE arising from the hybrid analysis never exceeds the index from MNA.  ...  The third author was supported by the European Union within the framework of the project "Integrated Circuit/EM Simulation and design Technologies for Advanced Radio Systems-on-chip" (FP7/2008/ICT/214911  ... 
doi:10.1007/978-3-642-12294-1_20 fatcat:2g64amagxzhhbfd4jxkv3bdeju

Convergence Analysis of Continuous Extension RKM for Index-1 DAE's

Wei Sun, Xiao-Guang Fan
2012 Procedia Engineering  
For solving nonlinear DAEs of index-1, the convergence results of the continuous extension Runge-Kutta methods are investigated.  ...  The methods are suitable for decoupling the complex, singular systems of instantaneous state.  ...  Introduction Nonlinear differential algebraic equations (DAEs) arise in connection with power systems, control theory, circuit simulations, robot dynamics, and many other applications in the fields of  ... 
doi:10.1016/j.proeng.2012.01.211 fatcat:jnxfzwhw6zd2ng4hkqxza5bc6m

Page 983 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Summary: “For index-1 DAEs with properly stated leading term, we characterize dissipative and contractive flows and study how the qualitative properties of the DAE solutions are reflected by numerical  ...  Summary: “For linear index-2 DAEs with properly stated leading term we characterize contractive and dissipative flows.  ... 

Verified Simulation of ODEs and DAEs in ValEncIA-IVP

Andreas Rauh, Ekaterina Auer
2011 Reliable Computing  
Especially for the simulation of asymptotically stable systems, we present a new exponential enclosure technique which describes contracting state enclosures.  ...  They also improve the performance of ValEncIA-IVP.  ...  Moreover, we extended its applicability to IVPs for DAEs and verified control synthesis. In future work, the DAE solver will be applied to further nonlinear system models.  ... 
dblp:journals/rc/RauhA11 fatcat:mnte4m52mzaxpn344drceocui4

Page 5321 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
On the Lie group analysis of linear systems of ODE. (English summary) Lie Groups Appl. 1 (1994), no. 2, 1-17.  ...  The index also is important in control and systems theory, but with different terminology. The consideration of increasingly complex nonlinear DAEs makes a clear and correct development necessary.  ... 

Page 7811 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
Here the contractivity of such methods, with regard to linear au- tonomous systems of ordinary differential equations and a (scaled) Euclidean norm, is studied.  ...  This paper deals with the stability analysis of theoretical and nu- merical solutions for a class of nonlinear neutral delay-differential equations (NDDEs).  ... 

Lagrange Stability of Semilinear Differential-Algebraic Equations and Application to Nonlinear Electrical Circuits

2018 Journal of Mathematical Physics, Analysis, Geometry  
The mathematical model of a radio engineering filter with nonlinear elements is studied as an application. The numerical analysis of the model verifies the results of theoretical investigations.  ...  We study a semilinear differential-algebraic equation (DAE) with the focus on the Lagrange stability (instability).  ...  The theorem on the Lagrange instability (Theorem 4.1) can be used, in particular, for the analysis of nonlinear control systems.  ... 
doi:10.15407/mag14.02.169 fatcat:uj2qukeayvdo5ed4htbz3llsyi

Autoencoder-Based Extrasystole Detection and Modification of RRI Data for Precise Heart Rate Variability Analysis

Koichi Fujiwara, Shota Miyatani, Asuka Goda, Miho Miyajima, Tetsuo Sasano, Manabu Kano
2021 Sensors  
In this study, we consider two types of extrasystoles—premature ventricular contraction (PVC) and premature atrial contraction (PAC)—which are types of extrasystoles that occur every day, even in healthy  ...  The RRI data are monitored by means of the AE in real time in the detection phase, and a denoising autoencoder (DAE) modifies the ectopic RRI caused by the detected extrasystole.  ...  LWPLS is an expansion of PLS based on the framework of Just-In-Time (JIT) [55] modeling for dealing with nonlinearity and system characteristics change [56, 57] .  ... 
doi:10.3390/s21093235 pmid:34067051 fatcat:3jifxfywxjdy5itzsic75o3fp4

Page 1710 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
Summary: “Contractivity properties of Runge-Kutta methods are analyzed, with a suitable interpolation implemented using a wave- form relaxation strategy for systems of ordinary differential equa- tions  ...  (I-LAQL-PM; L’Aquila) Contractivity of waveform relaxation Runge-Kutta iterations and related limit methods for dissipative systems in the maximum norm. (English summary) SIAM J. Numer.  ... 

Verified High-Order Integration of DAEs and Higher-Order ODEs [chapter]

Jens Hoefkens, Martin Berz, Kyoko Makino
2001 Scientific Computing, Validated Numerics, Interval Methods  
By rewriting this derivative-free system in a fixed point form, the solution can be obtained from a contracting Differential Algebraic operator in a finite number of steps.  ...  To this end, the highest derivative of the solution function occurring in either the ODE or the constraint conditions of the DAE is represented by a Taylor model.  ...  Moreover, the authors would like to thank John Pryce and George Corliss for valuable discussions and for bringing the problem of verified integration of DAEs to our attention.  ... 
doi:10.1007/978-1-4757-6484-0_23 fatcat:rbzsc5rc75ekfm2wo5l44x5moa

Numerical solution of nonlinear differential equations with algebraic constraints. I. Convergence results for backward differentiation formulas

Per L{ötstedt, Linda Petzold
1986 Mathematics of Computation  
In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints.  ...  Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from electrical networks, fluid dynamics and constrained mechanical systems  ...  Global Error Analysis for Index One and Two Nonlinear Systems.  ... 
doi:10.1090/s0025-5718-1986-0829621-x fatcat:buu4yvh6qbfvlk6mutmmwdwb2a

Table of Contents

2021 IEEE Transactions on Automatic Control  
Jiang 421 Contraction Analysis of Nonlinear DAE Systems. . . . . . . . . . . . . . . . .H. D. Nguyen, T. L. Vu, J.-J. Slotine, and K.  ...  Kamgarpour 413 Event-Triggered Stabilization of a Class of Nonlinear Time-Delay Systems . . . . . . . . . . . P. Zhang, T. Liu, and Z.-P.  ... 
doi:10.1109/tac.2020.3041692 fatcat:lk6is5co45gkxg3o5svddpp4pm
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