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.

Multiple Lyapunov Functions Analysis Approach for Discrete-Time-Switched Piecewise-Affine Systems Under Dwell-Time Constraints

Abstract: In this technical note, the asymptotic stability analysis and state-feedback control design are investigated for a class of discrete-time switched nonlinear systems via the smooth approximation technique. The modal dwell-time switching property is considered to constrain switchings between nonlinear subsystems. A kind of autonomous switchings, i.e., state-partition-dependent switching, is introduced within each approximated piecewise-affine (PWA) subsystem. Combining with the state partition information, the novel asymptotic stability conditions with less conservatism are derived for the induced switched PWA systems with dual switching mechanism based on the approach of multiple Lyapunov functions in piecewise quadratic form. Then, the design of PWA state-feedback controllers is implemented. The effectiveness of the obtained theoretical results is demonstrated by a numerical example.

Piecewise MILP under‐ and overestimators for global optimization of bilinear programs

Abstract: Many practical problems of interest in chemical engineering and other fields can be formulated as bilinear programs (BLPs). For such problems, a local nonlinear programming solver often provides a suboptimal solution or even fails to locate a feasible one. Numerous global optimization algorithms devised for bilinear programs rely on linear programming (LP) relaxation, which is often weak, and, thus, slows down the convergence rate of the global optimization algorithm. An interesting recent development is the idea of using an ab initio partitioning of the search domain to improve the relaxation quality, which results in a relaxation problem that is a mixed-integer linear program (MILP) rather than LP, called as piecewise MILP relaxation. However, much work is in order to fully exploit the potential of such approach. Several novel formulations are developed for piecewise MILP under- and overestimators for BLPs via three systematic approaches, and two segmentation schemes. As is demonstrated and evaluated the superiority of the novel models is shown, using a variety of examples. In addition, metrics are defined to measure the effectiveness of piecewise MILP relaxation within a two-level-relaxation framework, and several theoretical results are presented, as well as valuable insights into the properties of such relaxations, which may prove useful in developing global optimization algorithms. © 2008 American Institute of Chemical Engineers AIChE J, 2008

A Computational Framework for Determining Stereo Correspondence from a

Abstract: We present a computational framework for stereopsis based on the outputs of linear spatial filters tuned to a range of orientations and scales. This approach goes beyond edge-based and area-based approaches by using a richer image description and incorporating several stereo cues that previously have been neglected in the computer vision literature. A technique based on using the pseudo-inverse is presented for characterizing the information present in a vector of filter responses. We show how in our framework viewing geometry can be recovered to determine the locations of epipolar lines. An assumption that visible surfaces in the scene are piecewise smooth leads to differential treatment of image regions corresponding to binocularly visible surfaces, surface boundaries, and occluded regions that are only monocularly visible. The constraints imposed by viewing geometry and piecewise smoothness are incorporated into an iterative algorithm that gives good results on random-dot stereograms, artificially generated scenes, and natural grey-level images.