Generative Adversarial Networks have emerged as an effective technique for estimating data distributions. The basic setup consists of two deep networks playing against each other in a zero-sum game setting. However, it is not understood if the networks reach an equilibrium eventually and what dynamics makes this possible. The current GAN training procedure, which involves simultaneous gradient ...

The paper introduces, for age-distribution population vectors, a class of distances to the stable equivalent; each of these distances converges monotonically to zero as the population approaches stability. The Kullback distance, considered earlier to be unique as a measure with this property, turns out to be a mere specimen of this class. It is shown that the very feature of monotonic convergen...

This thesis is concerned with the control of highly uncertain systems. A formal theoretical explanation of the model-mismatch instability problem often associated with adaptive control design schemes is proposed, and a generic solution is provided. A primary task of adaptive control is formulated as finding an asymptotically optimal, stabilizing controller, given the feasibility of adaptive con...

the aim of this paper is to design a fractional order sliding mode controllers (fosmc)for a class of dc-dc converters such as boost and buck converters. firstly, the control lawis designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. secondly, themathematical proof of the stabilit...

the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton's method, but previous researchers have mentioned that some...

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...

A nonlinear chattering-free sliding mode control method is designed to stabilize fractional chaotic systems with model uncertainties and external disturbances. The main feature of this controller is rapid convergence to equilibrium point, minimize chattering and resistance against uncertainties. The frequency distributed model is used to prove the stability of the controlled system based on dir...

‎In this paper‎, ‎firstly‎, ‎we review approximation of fuzzy functions‎ ‎by fuzzy bicubic splines interpolation and present a new approach‎ ‎based on the two-dimensional fuzzy splines interpolation and‎ ‎iterative method to approximate the solution of two-dimensional‎ ‎linear fuzzy Fredholm integral equation (2DLFFIE)‎. ‎Also‎, ‎we prove‎ ‎convergence analysis and numerical stability analysis ...