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# SVM Viability Kernel Approximation (1/3)

## Description of the problem

The aim is to control a dynamical system such that it can survive inside a given set of admissible states *K*.

We consider a system defined by its state *x(t)* and controls *u(t)* (in discrete time, with set valued map *G*):

## Viability kernel

A state is called viable when there exists at least one control function for which the whole trajectory remains in *K*.

The viability kernel of the system is the set of all viable states

Viability kernel is instrumental to define viable control policies: the simplest rule, called heavy controller, is to change the control only when the system will cross the viability kernel boundary at the next time step.

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