Leveraging bifurcations for control of intelligent and collective behaviors

Motivation and Objectives 

From single-celled organisms to animal groups and human societies, living beings across scales sense their environment and react to it adaptively for survival. In doing so, they provide compelling examples of control systems capable of generating extremely robust and yet adaptable intelligent behaviors. Growing evidence has pointed to nonlinearity and, in particular, to bifurcations in nonlinear models as key ingredients for understanding the robust adaptability of these systems. To engineer autonomous systems that provably inherit the robust adaptability of their biological counterparts, control engineers must leverage these scientific insights and embrace bifurcation as a design principle. 

Bifurcations have a constructive role in natural and societal intelligence. A local bifurcation point is a parameter regime at which a solution of a nonlinear system changes stability. This is a point of ultra-sensitivity at which a control system can rapidly change its behavior in response to changes in the environment, even when those changes are arbitrarily small. This ultra-sensitivity can be observed in human decision-making, for example when a sudden event that requires a change in behavior happens while riding a bike or cooking a meal. Collective behaviors also exhibit ultra-sensitive responses, e.g., as a bacterial society does when antibiotics are poured into its environment, or as a human society can choose to do when imminent dangers are around the corner. Away from the ultra-sensitive bifurcation point, a control system ruled by bifurcations is organized into distinctively different robust behaviors associated with choosing a control action or strategy over alternative ones: steering the bike left instead of right into a pedestrian; turning the stove off instead of burning the sauce; developing a biofilm instead of remaining exposed to antibiotics; transitioning into a more sustainable lifestyle instead of doing business as usual. The co-existence of many different possible control choices is captured by the rich multi-stable attractor landscape that emerges at bifurcations. By navigating this landscape in response to inputs or in pursuit of goals, an agent can continuously adapt its behavior in a robust yet sensitive fashion. In other words, bifurcations can be leveraged for control to achieve robust and adaptive behaviors in ever-changing and unpredictable environments. This is diametrically opposed to the classical approach of controlled bifurcations for stabilization problems, in which a typical objective is to steer a system away from a bifurcation point, ideally achieving global stability.

To understand natural and societal collective and intelligent behaviors, and to draw inspiration from them for the design, analysis, and control of more robust and adaptable artificial intelligent and collective behaviors, a new synthesis of bifurcation and systems theories is needed. This workshop aims at providing the state-of-the art of recent efforts toward this new synthesis, and to explore new ideas toward its realization in applications.