ECOS-CONICYT C07E03: Viable control of discrete time systems and applications

AM2V Members: Pedro Gajardo
Start Date: 03-31-2008 - End Date: 02-28-2011
Status: finished

The general intention of this project is intention is to study some mathematical issues, concerning the viable control of discrete time systems, presented in the project MIFIMA: Mathematics, Informatics and FIsheries MAnagement (SticAmsud proposal).

Viability means the ability of survival, namely the capacity for a system to maintain, during time, condition of existence, good health, safety, or by extension, effectiveness (in the sense of cost-effectiveness in economics).

Viability issues arise obviously in engineering sciences and automatic control. Keeping a vehicle on a road, maintaining safety conditions in a industrial plant may constitute illustrations of viability problems.

The question of survival obviously arise in life sciences. The analysis of adaptative mechanisms adopted by a population with respect to its environment, the study of coexistence conditions for several species, the maintenance of biodiversity are preoccupations met by ecological and biological scientists, which are close to viability issues.

Also, viability issues are fundamental in the economic field through environmental and ecological economics. Harvesting a resource without exhausting it, preserving biodiversity, avoiding or mitigating climate change are examples of sustainability
concerns. More generally, the main question raised by sustainable development is how to reconcile economic growth and ecological conditions. The concepts of precaution, irreversibility, and intergenerational equity are closely related to viability issues. This implies to study the compatibility between biological, physical and economical dynamics, to mixconsiderations of ecologists, biologists, demographs and
economists and, in particular, to handle long term horizons.

The main common features of these problems are:

  • First, time plays a basic role. The state of some system evolves dynamically, with a certain control by decision makers.
  • Second, viability or a priori conditions are imposed to ensure a perennial behavior of the system. These are constraints that the state and the controls of the system have to satisfy during time.

These two point being stated, an important question arises quite
naturally: Which compatibility, if any, exists between the
dynamics of the system and these constraints? In other words, we have to study dynamical systems under constraints. In applied mathematics and system theory, this question has mostly been neglected to concentrate rather on steady state equilibria or optimization concepts.

The aim of this project is to provide mathematical tools to deal with dynamical systems under state and control constraints and to shed new lights on some applied viability problems especially in the economics and environmental fields.

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