Towards an operational definition of resilience for stochastic dynamical systems | Vers une définition opérationnelle de la résilience pour les systèmes dynamiques stochastiques

[Departement_IRSTEA]Ecotechnologies [TR1_IRSTEA]MOTIVE

International audience

English. Resilience, the capacity for a system to recover from a perturbation so as to keep its properties and functions, is of growing concern to a range of human and natural systems, especially those subjected to environmental variations. The challenge is often to make this concept operational without betraying it, nor diluting its content. The focus here is on systems that can be described by controlled discrete-time stochastic dynamics. Controls account for the possibility for the system to adapt to changes. The framework of viability theory for resilience, first defined in the deterministic case, is extended through the use of dynamic programming. This framework describes the essential properties of the system through a desirable set delimited by state constraints. It then states that a property is resilient to a perturbation if it can be recovered and kept by the system after a perturbation: its trajectory can come back and stay in the desirable set. With stochastic dynamics, maintaining forever the system in this set cannot be guaranteed in general, nor can we be sure that a trajectory will reach it. This motivates the definition of the notion of probability of resilience within a time horizon. It is the maximal probability that the system reaches a safe state, where it has a high probability of staying in the desirable set for a long time. Thus, resilience is computed by optimizing the control strategy, and this is achieved through dynamic programming. The proposed framework is shown to reflect a general definition of resilience while also leading to operational indexes that are intrinsically case-specific, such as statistics on the time of restoring the property.