Approximating Viability Kernels With Support Vector Machines

Deffuant, Guillaume; Chapel, Laëtitia; Martin, Sophie

doi:10.1109/tac.2007.895881

Cited by 46 publications

(43 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Dynamic programming is a recursive algorithm which enables to optimize a value function, noted V d (t, x) in this deterministic case, at each horizon t. It progresses backwards from date T (horizon 0) to the initial date (horizon T ). It yields the same results in the deterministic case as algorithms like KAVIAR [10] used by [11], but will be extended to the uncertain case in Section 3. Like any recursive algorithm, it works based on an initial equation and a transition equation.…”

Section: Viability-based De Nition Of Resiliencementioning

confidence: 88%

See 1 more Smart Citation

Extending the viability theory framework of resilience to uncertain dynamics, and application to lake eutrophication

Rougé¹,

Mathias²,

Deffuant³

2013

Ecological Indicators

Self Cite

View full text Add to dashboard Cite

)>IJH=?J 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. The challenge is often to render this concept operational without betraying it, nor diluting its content. The focus here is on building on the viability theory framework of resilience to extend it to discrete-time stochastic dynamical systems. The viability framework describes properties of the system as a subset of its state space. This 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 subset. This is shown to re ect a general de nition of resilience. With stochastic dynamics, the stochastic viability kernel describes the robust states, in which the system has a high probability of staying in the subset for a long time. Then, probability of resilience is de ned as the maximal probability that the system reaches a robust state within a time horizon. Management strategies that maximize the probability of resilience can be found through dynamic programming. It is then possible to compute a range of statistics on the time for restoring the property. The approach is illustrated on the example of lake eutrophication and shown to foster the use of di erent indicators that are adapted to distinct situations. Its relevance for the management of ecological systems is also discussed.

show abstract

Section: Viability-based De Nition Of Resiliencementioning

confidence: 88%

“…In practice, several algorithms exist to determine which states belong to the viability kernel [28,10].…”

Section: The Viability Kernelmentioning

confidence: 99%

Extending the viability theory framework of resilience to uncertain dynamics, and application to lake eutrophication

Rougé¹,

Mathias²,

Deffuant³

2013

Ecological Indicators

Self Cite

View full text Add to dashboard Cite

show abstract

“…To approximate the viability kernel of the Southern Benguela ecosystem, we use a new algorithm (Deffuant et al, 2007) (see Appendix 1) which is built on previous work from Saint-Pierre (1994), using a discrete approximation of the viability constraint set K by a grid.…”

Section: The Viability Analysis Control Problem and Viability Kernel mentioning

confidence: 99%

“…Mullon et al (2004) solved this problem with a method which is only adapted to linear equations of evolution. Here, we use a new method, based on support vector machines, which can be applied to non-linear models as well (Deffuant et al 2007). …”

Section: Introductionmentioning

confidence: 99%

Defining yield policies in a viability approach

Chapel¹,

Deffuant²,

Martin³

et al. 2008

Ecological Modelling

Self Cite

View full text Add to dashboard Cite

Mullon et al. (2004) proposed a dynamical model of biomass evolution in the Southern Benguela ecosystem, including five different groups (detritus, phytoplankton, zooplankton, pelagic fish and demersal fish). They studied this model in a viability perspective, trying to assess, for a given constant yield, whether each species biomass remains inside a given interval, taking into account the uncertainty on the interaction coefficients. Instead of studying the healthy states of this marine ecosystem with a constant yield, we focus here on the yield policies which keep the system viable. Using the mathematical concept of viability kernel, we examine how yield management might guarantee viable fisheries. One of the main practical difficulties up to now with the viability theory was the lack of methods to solve the problem in large dimensions. In this paper, we use a new method based on SVMs, which gives this theory a larger practical potential. Solving the viability problem provides all yield policies (if any) which guarantee a perennial system. We illustrate our main findings with numerical simulations.

show abstract

“…Saint-Pierre's algorithm computes for a given grid X h a discrete viability kernel that converges to the viability kernel when the grid resolution h tends to 0. Also several interesting results have recently appeared on numerical methods to compute viability kernels and capture basins [10], [5], [7] and [9]. Most of the time these approaches provide approximations based on the numerical diffusion induced by the discretization scheme.…”

Section: Introductionmentioning

confidence: 99%

Capture basin approximation using interval analysis

Lhommeau

Jaulin

Hardouin

2010

Adaptive Control & Signal

View full text Add to dashboard Cite

SUMMARYThis paper proposes a new approach for computing the capture basin C of a target T. The capture basin corresponds to the set of initial state vectors such that the target could be reached in finite time via an appropriate control input, before possibly leaving the target. Whereas classical capture basin characterization do not provide any guarantee on the set of state vectors that belong to the capture basin, interval analysis and guaranteed numerical integration allow us to avoid any indetermination. We present an algorithm able to provide guaranteed approximation of the inner C − and an the outer C + of the capture basin, such that C − ⊆ C ⊂ C + . In order to illustrate the principle and the efficiency of the approach, a testcase on the "car on the hill" problem is provided.

show abstract

Approximating Viability Kernels With Support Vector Machines

Cited by 46 publications

References 12 publications

Extending the viability theory framework of resilience to uncertain dynamics, and application to lake eutrophication

Extending the viability theory framework of resilience to uncertain dynamics, and application to lake eutrophication

Defining yield policies in a viability approach

Capture basin approximation using interval analysis

Contact Info

Product

Resources

About