wiki:SVM viability kernel approximation
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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):

$x(t+dt) = x(t) + \varphi(x(t), u(t))dt\hbox{, }\forall t \geq 0 $
$u(t) \in U(x(t)) $

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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