libhybrid - A library for discretized Hybrid Dynamical Systems

This library implements an hybrid system in the form:

$\begin{array}{rlr} \dot{t}(\tau) = & 1 & \text{for } (t, j, x, u) \in C \\ \dot{j}(\tau) = & 0 & \\ \dot{x}(\tau) = & f(t, j, x, u, p) & \\ \end{array}$

$\begin{array}{rlr} t^+(\tau) = & t & \text{for } (t, j, x, u) \in D \\ j^+(\tau) = & j + 1 & \\ x^+(\tau) = & g(t, j, x, u, p) & \\ \end{array}$

where:

f is the flow map;
g is the jump map;
h is the output map;
C is the flow set;
D is the jump set.
p are parameters.
is an engine time for the integration of t and j.

The flow map is discretized with a Runge Kutta 4 step. For the evolution of the system, both t and j are limited by horizons.