**ARGOMENTI:** International Area

ACPA-AM2V

Analysis of Control Problem with Applications ACT1106

Analysis and Mathematical Modeling Valparaíso

Departamento de Matemática, Universidad Técnica Federico Santa María

Avda. España 1680 - Valparaíso

Avda. Vicuña Mackenna 3939 - Santiago

B am2v@usm.cl

Postdoctoral research position

A postdoctoral research position is available at the Group Analysis and Mathematical Modeling Valparaíso in the

Departamento de Matemática at Universidad Técnica Federico Santa María. This position, funded by Anillo Project

ACT1106, is for one year, renewable for up to three years.

The Group is looking for a candidate holding a doctoral degree in applied mathematics, specialized in one of the

following (or related) areas:

Control of Partial differential equations and Inverse problems;

Optimization and variational analysis;

Numerical Analysis for optimization and control problems.

The candidate’s research record should include publications in international journals. A knowledge of Spanish is not

required. The candidate is expected to contribute with the research project with innovative ideas and publish in high-

quality journals. We offer a creative and social work environment, good opportunities for scientific development,

no teaching load and competitive gross salary1 (US$ 2.500 app. per month before taxes). Financial support for at

least one travel related to the scientific project each year, is also available. Further information about the AM2V’s

research and the Anillo Project can be found at www.am2v.cl

This position is available from March, 2013.

Applications should submit a Curriculum Vitae, copies of the most relevant publications, a short scientific project

related with the aims of the ACT1106 project (see Project Summary below), and at least one recommendation

letter before Jaunuary 10, 2012, to: am2v@usm.cl.

For further information, please contact am2v@usm.cl

1 As

a reference, the rent of a furnished apartment nearby the University campus is about US$ 700 per month.

PROJECT SUMMARY

ANILLO ACT110

Analysis of Control Problem with Applications - ACPA

Control Theory and related areas of mathematical analysis constitute extremely active fields of modern mathematics research.

These fields involve both profound theoretical challenges and applications in domains as diverse as biology, environmental

sciences, engineering, and others.

This proposal is concerned with the search for new and innovative mathematical tools and knowledge to analyze problems

that originate in real-world activities. In modern mathematics, these advances are often achieved by combining techniques

and ideas from two or more distinct areas of research. In this project, we plan to use our background in applied mathematics

to analyze specific problems, using interdisciplinary approaches: Optimization, Numerical Analysis, Inverse Problems, Control

of Partial Differential Equations, Mathematical Programming, and Optimal Control.

The main general objective of this proposal is to consolidate the scientific work of the researchers participating in this project

to establish the first research group in Chile focusing on theoretical control and optimization problems. This group will

become an important scientific center in our country, where the mathematical community currently comprises approximately

170 researchers. Funding of this proposal should have a significant impact on our small community.

The members of this project have a strong foundation in applied mathematics, modeling, and related fields. This background

will contribute to a multidisciplinary approach to identify solutions to applied mathematics problems. To fulfill the main

objective of this proposal, we present the Scientific Objectives that constitute the core of the scientific research proposed in

this project.

SO1. Control of bioprocesses. In classical macroscopic models of bioprocesses, the biomass is viewed as a catalyst for the

conversion of substrates into products. One key issue is the optimization of the production of the synthesis product

or biomass. We will address the issue of optimizing bioreactors using both approaches, optimal control and adaptive

control.

SO2. Sustainable exploitation of marine resources. Important fisheries are currently in a precarious situation. Mathematical

modeling can provide new and rigorous perspectives that can contribute to solutions. The models considered by

regulatory organisms are non-linear and age-structured, and they should be supported by experimental observations.

We plan to develop new theoretical tools in an effort to apply optimization and control techniques to realistic models.

SO3. Signal compression and recovery. The quality of signals depends on their storage and transmission, which usually

involves two major transformation steps: codification and reconstruction. Each of the two steps can be considered an

optimization problem. We plan to address this problem by applying constrained optimization algorithms to the original

infinite-dimensional signal spaces.

SO4. Control and inverse problems for Partial Differential Equations (PDEs). We primarily address controllability,

stabilization, and single-measurement inverse problems of PDEs. We will study the parameter-identification problems

of PDEs in relation to two kinds of mathematical models: those related to bioprocesses and fluid/solid problems in

biomechanics.

SO5. Numerical analysis of control problems. We intend to combine the expertise of the researchers concerning the control

theory with numerical techniques to develop discrete controls that converge to continuous controls. Furthermore, we

intend to develop new strategies that allow us to study analytical and numerical methods for control problems to

obtain convergence and optimal convergence rates in both open-loop and closed-loop cases.

SO6. Inverse problems in earth sciences. In asymptotic wind models, the necessary wind data is only known by measu-

rements at certain points. We plan to study the optimal control problem of identifying the closest solution of the

asymptotic model to these data. Another issue is the inverse problem of recovering the thickness of the plate from

partial bathymetric measures, which has been widely studied. We plan to consider this inverse problem from both

theoretical and numerical perspectives.

The scientific objectives mentioned below are oriented entirely toward the development of mathematical theory in an inter-

disciplinary framework.