Abstract

Biological entities can naturally be modeled as input-output systems with an internal dynamics defined by physical, chemical, and other biological processes. Inputs and outputs are defined by the interactions with the external world. Despite the abundance of elegant input-output behaviors to be studied in biology, connections between biology and control theory are still weak, essentially limited to genetic networks. The need for stronger interactions between biology and control theory is dictated by medical applications and by the development of performant biomorphic controllers.

Biological behaviors and biomedical control objectives involve intrinsically nonlinear phenomena: multi-stable switches, nonlinear oscillations, pattern formation, nonlinear traveling waves, just to name a few, and all behaviors possibly involving multiple spatiotemporal scales. Because present control theory is maturely developed only for linear behaviors (stable resting, tracking), a novel control theoretical paradigm is necessary to model biological behaviors and attack their robustness and modulation study.

Borrowing the concept of organizing center from singularity theory, I will propose a methodology to realize nonlinear behaviors from core circuits that reveal the fundamental role of monotonicity and feedback in their robustness and modulation. Motivated by neuroscience applications, I will introduce the core ideas of the theory on the robustness and modulation of bursting oscillations and bursting traveling waves.