ACPA

Aims and Scope

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.

These objectives can be summarized as:

  • Control of bioprocesses. 
  • Sustainable exploitation of marine resources. 
  • Signal compression and recovery. 
  • Control and inverse problems for Partial Differential Equations (PDEs). 
  • Numerical analysis of control problems. 
  • Inverse problems in earth sciences. 

Although the goals of this scientific research program are ambitious, these goals are consistent with our individual and joint collaborative experiences. Some of the problems stem naturally from our current research, whereas others involve entirely new challenges.

The scientific objectives mentioned below are oriented entirely toward the development of mathematical theory in an interdisciplinary framework. We must consider four Academic Objectives that are essential in achieving the main goals of the present project. These academic objectives allow us to consolidate our multidisciplinary team in several ways: first, by creating high-level scientific and technological research; second, by strengthening the expertise of young researchers in specific fields; third, by establishing and maintaining strong international networks; and, finally, by disseminating the results and knowledge acquired to the non-academic sectors.