A survey of applications of viability theory to the sustainable exploitation of renewable resources
In this paper, we survey the literature applying viability theory to the sustainable
management of renewable resources. After a refresher on the main concepts of viability …
management of renewable resources. After a refresher on the main concepts of viability …
Lagrangian methods for approximating the viability kernel in high-dimensional systems
While a number of Lagrangian algorithms to approximate reachability in dozens or even
hundreds of dimensions for systems with linear dynamics have recently appeared in the …
hundreds of dimensions for systems with linear dynamics have recently appeared in the …
Support vector machine informed explicit nonlinear model predictive control using low-discrepancy sequences
In this paper, an explicit nonlinear model predictive controller (ENMPC) for the stabilization
of nonlinear systems is investigated. The proposed ENMPC is constructed using tensored …
of nonlinear systems is investigated. The proposed ENMPC is constructed using tensored …
Solving viability problems in dynamic games using individual strategies derived from guaranteed viability kernels: Application to an agricultural cooperative model
S Martin, I Alvarez, F Lavallée - Automatica, 2024 - Elsevier
In this paper we address decentralized control problems in the context of sustainable
management of discrete-time deterministic dynamical systems. We consider N players, each …
management of discrete-time deterministic dynamical systems. We consider N players, each …
Extending the viability theory framework of resilience to uncertain dynamics, and application to lake eutrophication
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 wide range of environmental systems …
properties and functions, is of growing concern to a wide range of environmental systems …
Defining resilience mathematically: from attractors to viability
The previous chapter presents different views of resilience, starting from Holling's
conceptual definition of “ecological resilience”: the capacity of a system to absorb …
conceptual definition of “ecological resilience”: the capacity of a system to absorb …
Scalable safety-preserving robust control synthesis for continuous-time linear systems
We present a scalable set-valued safety-preserving hybrid controller for constrained
continuous-time linear time-invariant (LTI) systems subject to additive disturbance …
continuous-time linear time-invariant (LTI) systems subject to additive disturbance …
Computation of viability kernels: a case study of by-catch fisheries
Traditional means of studying environmental economics and management problems consist
of optimal control and dynamic game models that are solved for optimal or equilibrium …
of optimal control and dynamic game models that are solved for optimal or equilibrium …
Sustainability analysis: Viability concepts to consider transient and asymptotical dynamics in socio-ecological tourism-based systems
W Wei, I Alvarez, S Martin - Ecological Modelling, 2013 - Elsevier
With the increasing pressure on natural resources, the sustainability study of socio-
ecological systems has become a crucial scientific issue. In this paper we emphasize that …
ecological systems has become a crucial scientific issue. In this paper we emphasize that …
Computing an inner and an outer approximation of the viability kernel
The viability kernel corresponds to the set of all state vectors of a controlled dynamic system
that are viable, ie, such that there exists an input such that the system will not enter inside a …
that are viable, ie, such that there exists an input such that the system will not enter inside a …