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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TL;DR: A computationally inexpensive, yet high performance trajectory generation algorithm for omnidirectional vehicles that is based on a small number of evaluations of simple closed-form expressions and is thus extremely efficient.
234 citations
TL;DR: This work describes three possible piecewise multilinear hierarchical interpolation schemes in detail, and documents the features of the sparse grid interpolation software package spinterp for MATLAB.
Abstract: To recover or approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is preserved up to a logarithmic factor. We describe three possible piecewise multilinear hierarchical interpolation schemes in detail and conduct a numerical comparison. Furthermore, we document the features of our sparse grid interpolation software package spinterp for MATLAB.
233 citations
TL;DR: A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions.
Abstract: In this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, infin-norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory
233 citations
TL;DR: A new image encryption algorithm based on one-dimensional piecewise nonlinear chaotic maps that tries to improve the problem of failure of encryption such as small key space, encryption speed and level of security.
233 citations
TL;DR: An alternative formulation in which total variation is used as a constraint in a general convex programming framework is proposed, which places no limitation on the incorporation of additional constraints in the restoration process and the resulting optimization problem can be solved efficiently via block-iterative methods.
Abstract: Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective to be minimized under constraints. In this paper, we propose an alternative formulation in which total variation is used as a constraint in a general convex programming framework. This approach places no limitation on the incorporation of additional constraints in the restoration process and the resulting optimization problem can be solved efficiently via block-iterative methods. Image denoising and deconvolution applications are demonstrated.
233 citations