An indirect discretization method for fractional order PID controllers

C

Solving variational inequalities defined on a domain with infinitely many linear constraints

We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed method

On integrability of Hirota-Kimura type discretizations

We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.Comment: 47 pages, some minor change

A Non-parametric Semi-supervised Discretization Method

Semi-supervised classification methods aim to exploit labelled and unlabelled examples to train a predictive model. Most of these approaches make assumptions on the distribution of classes. This article first proposes a new semi-supervised discretization method which adopts very low informative prior on data. This method discretizes the numerical domain of a continuous input variable, while keeping the information relative to the prediction of classes. Then, an in-depth comparison of this semi-supervised method with the original supervised MODL approach is presented. We demonstrate that the semi-supervised approach is asymptotically equivalent to the supervised approach, improved with a post-optimization of the intervals bounds location