Algunos problemas en ecuaciones en derivadas parciales relacionados con la teoría de control

En esta memoria se abordan dos problemas relacionados con la teoría de control de ecuaciones en derivadas parciales.en el primer capitulo se estudia la controlabilidad aproximada de ecuaciones parabólicas semilineales y se obtienen tanto resultados de controlabilidad como contraejemplos. En el segundo se analiza la factorización de una ecuación elíptica lineal y se establece un paralelismo con la factorización lu del sistema discretizado correspondient

A Variance-Expected Compliance Model for Structural Optimization

t The goal of this paper is to find robust structures for a given main load and its perturbations. In the first part, we show the mathematical formulation of an original variance-expected compliance model used for structural optimization. In the second part, we study the interest of this model on two 3D benchmark test cases and compare the obtained results with those given by an expected compliance mode

A Multi-Layer Line Search Method to Improve the Initialization of Optimization Algorithms (Preprint submitted to Optimization Online)

We introduce a novel metaheuristic methodology to improve the initialization of a given deterministic or stochastic optimization algorithm. Our objective is to improve the performance of the considered algorithm, called core optimization algorithm, by reducing its number of cost function evaluations, by increasing its success rate and by boosting the precision of its results. In our approach, the core optimization is considered as a suboptimization problem for a multi-layer line search method. The approach is presented and implemented for various particular core optimization algorithms: Steepest Descent, Heavy-Ball, Genetic Algorithm, Differential Evolution and Controlled Random Search. We validate our methodology by considering a set of low and high dimensional benchmark problems (i.e., problems of dimension between 2 and 1000). The results are compared to those obtained with the core optimization algorithms alone and with two additional global optimization methods (Direct Tabu Search and Continuous Greedy Randomized Adaptive Search). These latter also aim at improving the initial condition for the core algorithms. The numerical results seem to indicate that our approach improves the performances of the core optimization algorithms and allows to generate algorithms more efficient than the other optimization methods studied here. A Matlab optimization package called ”Global Optimization Platform” (GOP), implementing the algorithms presented here, has been developed and can be downloaded at: http://www.mat.ucm.es/momat/software.ht

On the approximate controllability for higher order parabolic nonlinear equations of Cahn-Hilliard type

Sire prove the approximate controllability property for some higher order parabolic nonlinear equations of Cahn-Hilliard type when the nonlinearity is of sublinear type at infinity. We also give a counterexample showing that this property may fail when the nonlinearity is of superlinear type

Approximate controllability and obstruction phenomena for quasilinear diffusion equations

Symposium on Computational Science for the 21st-Century, Honoring Roland Glowinski on the Occasion of His 60th Birthday. Tours, MAY 05-07, 1997Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu

Asymptotic stability of a coupled Advection-Diffusion-Reaction system arising in bioreactor processes.

In this work, we perform an asymptotic analysis of a coupled system of two Advection-Diffusion-Reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacterias), called biomass, and a diluted organic contaminant (e.g., nitrates), called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the method of linearization to give sufficient conditions for the asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations

Modeling and optimization of activated sludge bioreactors for wastewater treatment taking into account spatial inhomogeneities

In this work, we study optimal and suboptimal control strategies for the treatment of a polluted water resource by using aside a continuous bioreactor. The control consists in choosing the inlet volumetric flow rate for filling the bioreactor with contaminated water from a considered resource (lake, reservoir, water-table, …). The treated outflow returns to the resource. We tackle an optimization problem which aims to minimize the time needed to reach a prescribed minimal value of contamination in the resource by choosing the input flow. Next, we study the influence of inhomogeneities of concentrations in the bioreactor, considering a system based on partial differential equations which describe its dynamics. We show that applying the optimal feedback control derived for perfectly mixed bioreactor does not allow to reach the target with small diffusion parameters as it drives the bioreactor to washout (the bioreactor equilibrium with no biomass). In this case, a suboptimal feedback (which reaches the target in finite time) is obtained with the help of a Hybrid Genetic Algorithm. Furthermore, we consider that the fluid flow velocity of the water entering into the bioreactor follows either a uniform or a nonuniform profile, showing that the optimal volumetric flow rates obtained with the uniform profile are not optimal if the profile is nonuniform, even when high diffusion coefficients are considered in the model

Solution landscapes in nematic microfluidics

We study the static equilibria of a simplified Leslie–Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient G and inverse anchoring strength, B. We numerically find multiple static equilibria for admissible pairs (G,B) and classify them according to their winding numbers and stability. The case G=0 is analytically tractable and we numerically study how the solution landscape is transformed as G increases. We study the one-dimensional dynamical model, the sensitivity of the dynamic solutions to initial conditions and the rate of change of G and B. We provide a physically interesting example of how the time delay between the applications of G and B can determine the selection of the final steady state

Un problema inverso emergente en el estudio de los movimientos con rotaciones intrínsecas no coaxiales de un disco

Se aborda el problema inverso de hallar el vector velocidad angular ωb(t) caracterizando el movimiento de rotación de un sólido rígido del que se conoce la descripción de las velocidades. Tal cuestión est´a motivada por el comportamiento observado sobre ciertos prototipos construidos por Advanced Dynamics S.A. Aunque la cuestión planteada puede ser abordada mediante "técnicas de eliminación” para sistemas semiimplícitos asociados a problemas de controlabilidad no lineal, al tomar como control el vector velocidad angular ωb(t) ([2] F. Bonnans and P. Rouchon, Commande et optimisation de systèmes dynamiques, Editions de l’École Polytechnique, Palaiseau, 2005, [3] H.J. Khalil, Nonlinear Systems, Second edition, Prentice Hall, Upper Saddle River, NJ, 1996), aquí seguimos un proceso enteramente original y distinto consistente en la aplicación de un proceso iterativo basado en la inversión de las ecuaciones diferenciales implicadas

Final validation of the forecast for the spread of the Ebola virus disease 2018-20 (EVD 2018-20) done with the Be-CoDiS mathematical model

Depto. de Análisis Matemático y Matemática AplicadaInstituto de Matemática Interdisciplinar (IMI)Fac. de Ciencias MatemáticasFALSEMinisterio de Economía y Competitividad (MINECO)unpu