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Recent works have demonstrated how Linear Parameter Varying Model Predictive Control (LPV MPC) algorithms are able to control nonlinear systems with precision and reduced computational load. Specifically, these schemes achieve comparable performances to state-of-the-art nonlinear MPCs, while requiring the solution of only one quadratic programming problem (thus being real-time capable). In this tutorial paper, we provide a step-by-step overview of how to implement such LPV MPC algorithms, covering from modelling to stability aspects. For illustration purposes, we consider a realistic implementation for a gas-lift petroleoum extraction process, comparing the LPV approach with the becnhmark nonlinear MPC software CasADi., Comment: Main text in portuguese, submitted to the 2023 Simp\'osio Brasileiro de Automa\c{c}\~ao Inteligente (SBAI 2023)

In this paper we present modern portfolio theory using basic concepts of linear algebra, differential calculus, statistics and optimization. This theory allows us to measure the return and risk of the investment portfolio, helping to make decisions in the financial market. As an application, we will present a simple investment strategy that aims to minimize the risk of investing in two assets, Comment: 31 pages, in Portuguese language, 13 figures

Vehicle Routing Problems are problems in which a set of customers is visited by a set of vehicles. In this work, we model a multiobjective benchmark on a 2D map based on a realistic routing problem of food deliveries by motorcycles in the city of Rio Claro-SP. The generated map of Rio Claro presents 1566 streets with manually extracted coordinates and modeled through polygonal chains. We generate a total of 23 instances containing 2 to 7 deposits and up to 2000 delivery points. This work is an extension of \cite{2020zeni} in which the authors model the problem of mail delivery by postmen in the city of Artur Nogueira. The research of Zeni et al. has one deposit, while in this work we have multiple deposits. In Zeni et al., the city of Artur Nogueira was modeled, with 537 streets. In this work, a map of Rio Claro is modeled, with 1566 streets., Comment: in Portuguese

There is a great need to stock materials for production, but storing materials comes at a cost. Lack of organization in the inventory can result in a very high cost for the final product, in addition to generating other problems in the production chain. In this work we present mathematical and statistical methods applicable to stock management. The stock analysis using ABC curves serves to identify which are the priority items, the most expensive and with the highest turnover (demand), and thus determine, through stock control models, the purchase lot size and the periodicity that minimize the total costs of storing these materials. Using the Economic Order Quantity (EOQ) model and the (Q,R) model, the inventory costs of a company were minimized. The comparison of the results provided by the models was performed., Comment: In Portuguese, 17 pages, 12 figures, 7 tables. Conference SEMAT2017

(English) In a previous work [Nonlinearity, 20:2271-2287, 2007; arXiv:math/0703895] it is investigated, by means of computational simulations, shapes of nonconvex bodies that maximize resistance to its motion on a rarefied medium, considering that bodies are moving forward and at the same time slowly rotating. Here the previous results are improved: we obtain a two-dimensional geometric shape that confers to the body a resistance very close to the supremum value (R=1.4965, Comment: 32 pages, in Portuguese

English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking, nonlinear, and very hard to solve. One way to address the problem is to obtain conservation laws of lower order than those of the corresponding Euler-Lagrange equations. While in Physics and Economics the question of existence of conservation laws is treated in a rather natural way, because the application itself suggest the conservation laws (e.g., conservation of energy, income/health law), from a strictly mathematical point of view, given a problem of the calculus of variations, it is not obvious how one might derive a conservation law or, for that matter, if it even has a conservation law. The question we address is thus to develop computational facilities, based on a systematic method, which permits to identify functionals that have conservation laws. The central result we use is the celebrated Noether's theorem. This theorem links conservation laws with the invariance properties of the problem (with symmetries), and provides an algorithm for finding conservation laws. Thus the problem is reduced to the one of finding the variational symmetries. We show how a Computer Algebra System can help to find the symmetries and the conservation laws in the calculus of variations. Several illustrative examples are given., 20 pages, in Portuguese. Partially presented at XXVII CNMAC (Brazilian Congress of Applied Mathematics and Computation), FAMAT/PUCRS, Porto Alegre, RS, Brasil, 13-16 September 2004. Supported by the program PRODEP III/5.3/2003 and the R&D unit CEOC of the University of Aveiro

A formula for the Riemannian metric tensor of differentiable manifolds of linear dynamical systems of same McMillan degree is presented in terms of their transfer function matrices. The necessary calculations for its application to ARMA and state space overlapping parametrizations are drafted. The importance of this approach for systems identification and multiple time series analysis and forecasting is explained., 3 pages in portuguese, reference links to author's detailed proofs in english