Structural Analysis: The Control Language to Understand Mechanisms

Abstract

Mathematics plays a fundamental role in disciplines such as physics, engineering, computer science, and chemistry and has been more recently accepted as a suitable language for solving problems in biology, biochemistry, and medicine.

Control theory is part of the mathematical world and has the peculiarity of borrowing tools from different branches of mathematics. Interestingly, many of the techniques conceived and routinely used to solve control problems can be quite successfully adapted to solve new relevant problems, both practical and curiosity-driven, in other fields.

This talk discusses the structural analysis of systems, aimed at explaining how mechanisms work, why they work in a certain way, and to which extent they perform their task properly even in the presence of perturbations and disturbances.

The first part of the talk briefly introduces some preliminary motivating examples of mechanisms, borrowed from other disciplines alien to control theory, to show how a control approach can be very powerful to understand fundamental principles.

The second part introduces the definitions of structural versus robust properties, discussing paradigmatic case studies from the literature. Robust stability analysis is presented in an inverse form: "We know that this system is stable, but why is the system so incredibly stable?". Other fundamental concepts such as (perfect) adaptation, structural steady-state analysis, graph loop analysis, and aggregation are considered.

The third part discusses application examples from biology and biochemistry, to showcase the potential impact that the mathematical approach of control theory, suitably revised, can have in these disciplines and how interdisciplinary research can bring fresh ideas to control theorists.