This article presents an analysis of the chaotic dynamics presented by the Lorenz system and how this behavior can be eliminated through the implementation of sliding mode control. It is necessary to know about the theory of stability of Lyapunov to develop the appropriate control that allows to bring the system to the desired point of operation.
The purpose of this paper is to present the capabilities of the conjugate gradient methods based on the theoretical analysis of the gradient method, the precursor of the descent methods. It indicates the geometric differences of these and the improvements made in the search for the optimal value of an objective function. Different test systems are proposed to solve, in order to obtain a solution that can determine the speed of convergence of the conjugate address proposed by Liu-Storey and Dai-Yuan [1].
Finding the electrostatic potential produced by a point load is an easy task, when that point load is replaced by a load distribution this task is complicated, the difficulty of this procedure depends on the place where you want to know the potential, it is not the same to find the potential at a given point to find it in any place in space. In this case we will work with a uniformly charged two-dimensional ring, the problem that arises is the obtaining of the electrostatic potential at any point around the ring, for this we will look for the conditions that must be met to pose the problem, a theoretical solution for this problem, in which we find the Legendre polynomials and finally proceeds to make this same solution using the two dimensional finite element method.
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