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### Operational Models for Piecewise-Smooth Systems

Andrew Sogokon, Khalil Ghorbal, Taylor T. Johnson
2017 ACM Transactions on Embedded Computing Systems
In this article we study ways of constructing meaningful operational models of piecewise-smooth systems (PWS).  ...  The different ways of building operational models that we explore in our approach can be thought of as defining different semantics for the underlying PWS.  ...  for pointing out some relevant references.  ...

### Modelling localized nonlinearities in continuous systems via the method of augmentation by non-smooth basis functions

M. R. Brake, D. J. Segalman
2013 Proceedings of the Royal Society A
Existing solutions for continuous systems with localized, non-smooth nonlinearities (such as impacts) focus on exact methods for satisfying the nonlinear constitutive equations.  ...  Exact methods often require that the non-smooth nonlinearities be expressed as piecewise-linear functions, which results in a series of mapping equations between each linear regime of the nonlinearities  ...  Bond and Kurtis Ford for their feedback and support.  ...

### Some New Circuit Design for Chaos Generation [chapter]

K. S. Tang, K. F. Man, G. Q. Zhong, G. Chen
2002 World Scientific Series on Nonlinear Science Series B
This chapter discusses some new circuitry design of chaos generation in simple three-dimensional autonomous systems. The well-known Chua's circuit will be adopted as the framework for basic design.  ...  Finally, a circuit design for realizing Chen's chaotic attractor, generated by simple smooth quadratic functions, is suggested.  ...  Mathematical model of the system The mathematical model of the chaotic Chen's attractor is described by the following state equations:ẋ = a(y − x) , y = (c − a)x − xz + cy , z = xy − bz , (9.4.9) where  ...

### Modeling and simulating cyber-physical systems using CyPhySim

Edward A. Lee, Mehrdad Niknami, Thierry S. Nouidui, Michael Wetter
2015 2015 International Conference on Embedded Software (EMSOFT)
It includes an innovation called "smooth tokens," which allow for a blend of numerical and symbolic computation, and for certain kinds of system models, dramatically reducing the computation required for  ...  (FMI) for model-exchange and co-simulation, discrete-time (periodic) systems, and algebraic loop solvers.  ...  Each state represents a mode of operation. The model for each mode is given as a refinement of the states.  ...

### Image restoration: A wavelet frame based model for piecewise smooth functions and beyond

Jian-Feng Cai, Bin Dong, Zuowei Shen
2016 Applied and Computational Harmonic Analysis
Our numerical studies show that the proposed model is the right one for image restorations, when the underlying solutions are piecewise smooth.  ...  To further understand the piecewise smooth nature of the obtained solutions, we connect it to a variational model on the space of piecewise smooth functions and prove rigorously that the discrete model  ...  Wavelet Frame Based Model for Piecewise Smooth Functions In this section, we present our wavelet frame based image restoration model for piecewise smooth functions.  ...

### Page 6365 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews
Summary: “We discuss piecewise smooth solutions for semilinear hyperbolic systems in multi-dimensional space.  ...  and estimates of jump discontinuities, a result on reflection of singularities for piecewise smooth solutions corresponding to piecewise smooth initial values.  ...

### An Improved Algorithm for the Piecewise-Smooth Mumford and Shah Model in Image Segmentation

Yingjie Zhang
2006 EURASIP Journal on Bioinformatics and Systems Biology
An improved algorithm for the piecewise-smooth Mumford and Shah functional is presented.  ...  MUMFORD-SHAH MODEL The Mumford-Shah model is a variational problem for approximating a given image by a piecewise smooth image of minimal complexity.  ...  Since the evolution of curves coupled with diffusion in the piecewise-smooth MS model, the resulting image might become very homogeneous in certain iterations.  ...

### Recovery of piecewise smooth images from few fourier samples

Greg Ongie, Mathews Jacob
2015 2015 International Conference on Sampling Theory and Applications (SampTA)
We introduce a Prony-like method to recover a continuous domain 2-D piecewise smooth image from few of its Fourier samples.  ...  We present necessary and sufficient conditions for unique recovery of piecewise constant images using the above annihilation relation.  ...  As described above, this signal model is not very realistic for natural images. 3) Piecewise harmonic: Both the above cases consider only first-order differenial operators.  ...

### Learning smooth models of nonsmooth functions via convex optimization

F. Lauer, V.L. Le, G. Bloch
2012 2012 IEEE International Workshop on Machine Learning for Signal Processing
This paper proposes a learning framework and a set of algorithms for nonsmooth regression, i.e., for learning piecewise smooth target functions with discontinuities in the function itself or the derivatives  ...  In the proposed approach, the model belongs to a class of smooth functions.  ...  Piecewise smooth dynamical system identification -1-4673-1026-0/12/\$31.00 c 2012 IEEE  ...

### Continuously Differentiable Analytical Models for Implicit Control within Power Flow [article]

Aayushya Agarwal, Amritanshu Pandey, Marko Jereminov, Larry Pileggi
2018 arXiv   pre-print
unstable operational region.  ...  One specific issue relates to the disconnected solution space that is created by the use of piecewise-discontinuous models of power grid devices that perform control mechanisms.  ...  Issues with Piecewise Models Using piecewise continuous models that are not firstderivative continuous within nonlinear system solvers relies on stringent conditions for convergence [20] .  ...

### Total Bending Method for Piecewise Smoothing Image Denoising

Bibo Lu, Zhenzhen Huangfu, Rui Huang
2019 Mathematical Problems in Engineering
Since the seminar work by Rudin, Osher, and Fatami for total variation (TV) model, piecewise smoothing image is favored in a diversity of related fields.  ...  To recover a piecewise smoothing image, we propose a high order anisotropic geometrical model which we name total bending (TB) in a multiplicative strategy.  ...  First order operator based models, such as TV, can recover a piecewise constant image while performing poor for smoothing transition region recovering [1] .  ...

### On Computational Issues of Market-Based Optimal Power Flow

Hongye Wang, Carlos E. Murillo-Sanchez, Ray D. Zimmerman, Robert J. Thomas
2007 IEEE Transactions on Power Systems
The deregulated electricity market calls for robust optimal power flow (OPF) tools that can provide a) deterministic convergence; b) accurate computation of nodal prices; c) support of both smooth and  ...  The new formulations and algorithms, along with several existing ones, are tested and compared using large-scale power system models.  ...  Instead, system operators often use simplified OPF tools that are based on linear programming (LP) and decoupled (DC) system models [14] .  ...

### Analysis of Linear Piecewise Constant Delay Systems Using a Hybrid Numerical Scheme

H. R. Marzban, S. M. Hoseini
2016 Advances in Numerical Analysis
A key feature of the proposed framework is the excellent representation of smooth and especially piecewise smooth functions.  ...  An efficient computational technique for solving linear delay differential equations with a piecewise constant delay function is presented.  ...  Owing to the nature of DDEs, none of the smooth basis functions is able to properly model the inherent behavior of this class of systems.  ...

### Linearization modeling for non-smooth dynamical systems with approximated scalar sign function

Jian Zhang, Yongpeng Zhang, Warsame Ali, Leang-san Shieh
2011 IEEE Conference on Decision and Control and European Control Conference
Through the proposed methodology, the non-smooth dynamical system model can be transformed into a universal and smooth model.  ...  Thus, the following optimal linearization can be applied to obtain the local linear model at any operating point.  ...  Section III introduces the optimal linearization method for the resulting smooth system model.  ...

### Robust moving least-squares fitting with sharp features

Shachar Fleishman, Daniel Cohen-Or, Cláudio T. Silva
2005 ACM SIGGRAPH 2005 Papers on - SIGGRAPH '05
We introduce a robust moving least-squares technique for reconstructing a piecewise smooth surface from a potentially noisy point cloud.  ...  of the projection operator.  ...  The drill model is courtesy of Sergei Azernikov (Technion -Israel Institute of Tech- nology). We thank Elaine Cohen and Ross Whitaker for use of the Deltasphere TM scanner.  ...
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