Viabilitree: A kd-tree Framework for Viability-based Decision

The mathematical viability theory offers concepts and methods that are suitable to study the compatibility between a dynamical system described by a set of differential equations and constraints in the state space. The result sets built during the viability analysis can give very useful information regarding management issues in fields where it is easier to discuss constraints than objective functions. However, computational problems arise very quickly with the number of state variables, and the practical implementation of the method is difficult, although there exists a convergent numerical scheme and several approaches to bypass the computational problems. In order to popularize the use of viability analysis we propose a framework in which the viability sets are represented and approximated with particular kd-trees. The computation of the viability kernel is seen as an active learning problem. We prove the convergence of the algorithm and assess the approximation it produces for known problems with analytical solution. This framework aims at simplifying the declaration of the viability problem and provides useful methods to assist further use of viability sets produced by the computation.

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