ENTEG Guest Seminar by Prof Franco Blanchini

ENTEG Guest Seminar by Prof. Franco Blanchini

Robust or structural?

Many natural systems are amazingly robust with respect to noise, parameter variations, and environmental changes. One of the most important objectives in systems biology is to explain why this can happen. This type of analysis is a perfect field of application for most of the mathematical techniques developed in control theory. The first part of this presentation is a tutorial discussion of the possible paradigms and questions about robustness that can be addressed by means of fairly standard control engineering techniques. We say that a property pertaining to a system is robust if it persists under large parameter variations, within suitable numerical bounds. Conversely, the property is structural if it is satisfied by a class of systems regardless of parameter values. The second part of the talk is more technical. We consider a large class of systems admitting the so-called BDC decomposition, which captures the system structure and isolates the uncertain or unknown parameters. Most biochemical, gene, metabolic networks admit such a structural representation. We consider various properties such as boundedness, stability, multi-stability, existence of equilibria, adaptation, long term influence, oscillatory behaviour, and we present several techniques to structurally assess these properties based on time-scale separation, Lyapunov theory, parametric uncertainty, graph theory, positive invariance.