[1][2] It was developed to formalize problems arising in the study of various natural and social phenomena, and has close ties to the theories of optimal control and set-valued analysis.
Viability theory started in 1976 by translating mathematically the title of the book Chance and Necessity[3] by Jacques Monod to the differential inclusion
They share common features: Viability theory thus designs and develops mathematical and algorithmic methods for investigating the "adaptation to viability constraints" of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences.
The viability kernel assumes that some kind of "decision maker" controls or regulates evolutions of the system.
If not, the next problem looks at the "tychastic kernel" (from tyche, meaning chance in Greek) or "invariance kernel", the subset of initial states in the environment such that all evolutions are "viable" in the environment, an alternative way to stochastic differential equations encapsulating the concept of "insurance" against uncertainty, providing a way of eradicating it instead of evaluating it.