Geometric Robustness of Viability Kernels and Resilience Basins

Alvarez, Isabelle; Martin, Sophie

doi:10.1007/978-3-642-20423-4_8

Cited by 4 publications

(6 citation statements)

References 7 publications

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“…Viability theory makes it possible to define resilience without reverting to the concept of a steady state (Martin, 2004;Martin et al, 2011), and to define robustness against state uncertainty (Alvarez and Martin, 2011;Rougé et al 2013). In our study, we further developed this approach and showed how viability could be used to define robustness against dynamic stochasticity and management adaptability.…”

Section: Discussionmentioning

confidence: 99%

“…Robustness measures how likely the system, in a certain state with a certain control, is to remain in desirable conditions in an uncertain environment . Alvarez and Martin (2011) formalized this idea in the case where uncertainty applies directly to the state determination and define robustness of a state as its distance to the boundary of the viability kernel (or resilience basin). In this study, we measure robustness as the probability of a control to keep the system in a viable state.…”

Section: Adaptability and Robustness In Rangelandsmentioning

confidence: 99%

“…This index represents the probability that being in the state s and applying the control c, the system stays in a viable state (Rougé et al, 2013). This index is an adaptation of the robustness index developed by Alvarez and Martin (2011) to the situation where stochasticity occurs as a perturbation of the dynamics rather than a direct perturbation of the state.…”

Section: Adaptability and Robustness In Rangelandsmentioning

confidence: 99%

See 2 more Smart Citations

Robustness and management adaptability in tropical rangelands: a viability-based assessment under the non-equilibrium paradigm

Accatino

Sabatier

Michele

et al. 2014

Animal

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Rangelands provide the main forage resource for livestock in many parts of the world, but maintaining long-term productivity and providing sufficient income for the rancher remains a challenge. One key issue is to maintain the rangeland in conditions where the rancher has the greatest possibility to adapt his/her management choices to a highly fluctuating and uncertain environment. In this study, we address management robustness and adaptability, which increase the resilience of a rangeland. After reviewing how the concept of resilience evolved in parallel to modelling views on rangelands, we present a dynamic model of rangelands to which we applied the mathematical framework of viability theory to quantify the management adaptability of the system in a stochastic environment. This quantification is based on an index that combines the robustness of the system to rainfall variability and the ability of the rancher to adjust his/her management through time. We evaluated the adaptability for four possible scenarios combining two rainfall regimes (high or low) with two herding strategies (grazers only or mixed herd). Results show that pure grazing is viable only for high-rainfall regimes, and that the use of mixed-feeder herds increases the adaptability of the management. The management is the most adaptive with mixed herds and in rangelands composed of an intermediate density of trees and grasses. In such situations, grass provides high quantities of biomass and woody plants ensure robustness to droughts. Beyond the implications for management, our results illustrate the relevance of viability theory for addressing the issue of robustness and adaptability in non-equilibrium environments.

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Section: Discussionmentioning

confidence: 99%

Section: Adaptability and Robustness In Rangelandsmentioning

confidence: 99%

Section: Adaptability and Robustness In Rangelandsmentioning

confidence: 99%

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Robustness and management adaptability in tropical rangelands: a viability-based assessment under the non-equilibrium paradigm

Accatino

Sabatier

Michele

et al. 2014

Animal

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“…This approach to a goodness function is similar to the one developed in [33] in the context of viability theory, where the distance from the undesirable set is considered as an indicator of a trajectory robustness. Since in our case we are interested in measuring the "robustness" (i.e., goodness) of our prediction of the future trajectory, we replace the distance from the undesirable set by the rate of change of the distance.…”

Section: Measuring Goodnessmentioning

confidence: 99%

Control-Oriented Learning on the Fly

Ornik

Carr

Israel

et al. 2020

IEEE Trans. Automat. Contr.

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This paper focuses on developing a strategy for control of systems whose dynamics are almost entirely unknown.This situation arises naturally in a scenario where a system undergoes a critical failure. In that case, it is imperative to retain the ability to satisfy basic control objectives in order to avert an imminent catastrophe. A prime example of such an objective is the reach-avoid problem, where a system needs to move to a certain state in a constrained state space. To deal with limitations on our knowledge of system dynamics, we develop a theory of myopic control.The primary goal of myopic control is to, at any given time, optimize the current direction of the system trajectory, given solely the information obtained about the system until that time. We propose an algorithm that uses small perturbations in the control effort to learn local dynamics while simultaneously ensuring that the system moves in a direction that appears to be nearly optimal, and provide hard bounds for its suboptimality. We additionally verify the usefulness of the algorithm on a simulation of a damaged aircraft seeking to avoid a crash, as well as on an example of a Van der Pol oscillator.

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“…Unfortunately these strategies often lead trajectories to the boundary of the viability kernel, which is not desirable, since outside the viability kernel trajectories are doomed to leave the constraint set. Heuristic prudent trajectories [1] can be considered to stay far from the boundary, but the computation of trajectories robust to perturbation is very time consuming [28].…”

Section: Introductionmentioning

confidence: 99%

Towards Evolutionary Control Laws for Viability Problems

Tonda

Alvarez

Martin

et al. 2023

Proceedings of the Genetic and Evolutionary Computation Conference

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The mathematical theory of viability, developed to formalize problems related to natural and social phenomena, investigates the evolution of dynamical systems under constraints. A main objective of this theory is to design control laws to keep systems inside viable domains. Control laws are traditionally defined as rules, based on the current position in the state space with respect to the boundaries of the viability kernel. However, finding these boundaries is a computationally expensive procedure, feasible only for trivial systems. We propose an approach based on Genetic Programming (GP) to discover control laws for viability problems in analytic form. Such laws could keep a system viable without the need of computing its viability kernel, facilitate communication with stakeholders, and improve explainability. A candidate set of control rules is encoded as GP trees describing equations. Evaluation is noisy, due to stochastic sampling: initial conditions are randomly drawn from the state space of the problem, and for each, a system of differential equations describing the system is solved, creating a trajectory. Candidate control laws are rewarded for keeping viable as many trajectories as possible, for as long as possible. The proposed approach is evaluated on established benchmarks for viability and delivers promising results.

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Geometric Robustness of Viability Kernels and Resilience Basins

Cited by 4 publications

References 7 publications

Robustness and management adaptability in tropical rangelands: a viability-based assessment under the non-equilibrium paradigm

Robustness and management adaptability in tropical rangelands: a viability-based assessment under the non-equilibrium paradigm

Control-Oriented Learning on the Fly

Towards Evolutionary Control Laws for Viability Problems

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