Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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24 Jul 2005
TL;DR: In this article, the authors proposed a continuous differentiable model for friction, which represents a foundation that captures the major effects reported and discussed in friction modeling and experimentation and is generic enough that other subtleties such as frictional anisotropy with sliding direction can be addressed by mathematically distorting this model.
Abstract: For high-performance engineering systems, model-based controllers are typically required to accommodate for the system nonlinearities. Unfortunately, developing accurate models for friction has been historically challenging. Typical models are either discontinuous and many other models are only piecewise continuous. Motivated by the fact that discontinuous and piecewise continuous friction models are problematic for the development of high-performance continuous controllers, a new model for friction is proposed in this paper. This simple continuously differentiable model represents a foundation that captures the major effects reported and discussed in friction modeling and experimentation. The proposed model is generic enough that other subtleties such as frictional anisotropy with sliding direction can be addressed by mathematically distorting this model without compromising the continuous differentiability
207 citations
TL;DR: In this paper, a level set approach for elliptic inverse problems with piecewise constant coefficients is proposed, where the geometry of the discontinuity of the coefficient is represented implicitly by level set functions.
207 citations
TL;DR: In this article, the authors propose a method for reconstructing blocky conductivity profiles in electrical impedance tomography, which is based on selecting a conductivity distribution that has the least total variation from all conductivities that are consistent with the measured data.
Abstract: We propose an idea for reconstructing 'blocky' conductivity profiles in electrical impedance tomography. By 'blocky' profiles, we mean functions that are piecewise constant, and hence have sharply defined edges. The method is based on selecting a conductivity distribution that has the least total variation from all conductivities that are consistent with the measured data. We provide some motivation for this approach and formulate a computationally feasible problem for the linearized version of the impedance tomography problem. A simple gradient descent-type minimization algorithm, closely related to recent work on noise and blur removal in image processing via non-linear diffusion is described. The potential of the method is demonstrated in several numerical experiments.
207 citations
TL;DR: In this paper, a low-order panel method is presented for the calculation of subsonic aerodynamic characteristics of general configurations, based on piecewise constant doublet and source singularities.
Abstract: A low-order panel method is presented for the calculation of subsonic aerodynamic characteristics of general configurations. The method is based on piecewise constant doublet and source singularities. Two forms of the internal Dirichlet boundary condition are discussed and the source distribution is determined by the external Neumann boundary condition. Calculations are compared with higher-order solutions for a number of cases. It is demonstrated that for comparable density of control points where the boundary conditions are satisfied, the low-order method gives comparable accuracy to the higher-order solutions. It is also shown that problems associated with some earlier low-order panel methods, e.g., leakage in internal flows and junctions and also poor trailing-edge solutions, do not appear for the present method. Further, the application of the Kutta condition is extremely simple; no extra equation or trailing-edge velocity point is required. The method has very low computing costs and this has made it practical for application to nonlinear problems requiring iterative solutions and to three-dimensional unsteady problems using a time-stepping approach. In addition, the method has been extended to model separated flows in three dimensions, using free vortex sheets to enclose the separated zone.
205 citations
TL;DR: Two new approaches to the reliable SOF controller analysis and synthesis are proposed for the underlying stochastic fuzzy-affine systems based on a Markovian Lyapunov function combined with Itô differential formula, S-procedure, and some matrix inequality convexification procedures.
Abstract: This paper deals with the problem of reliable and robust $\mathscr {H}_{\infty }$ static output feedback (SOF) controller synthesis for continuous-time nonlinear stochastic systems with actuator faults. The nonlinear stochastic plant is expressed by an Ito-type Takagi–Sugeno fuzzy-affine model with parametric uncertainties, and a Markov process is employed to model the occurrence of actuator fault. The purpose is to design an admissible piecewise SOF controller, such that the resulting closed-loop system is stochastically stable with a prescribed disturbance attenuation level in an $\mathscr {H}_{\infty }$ sense. Specifically, based on a Markovian Lyapunov function combined with Ito differential formula, S-procedure, and some matrix inequality convexification procedures, two new approaches to the reliable SOF controller analysis and synthesis are proposed for the underlying stochastic fuzzy-affine systems. It is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness and advantages of the developed methods.
205 citations