Author

Matteo Ragni, Matteo Cocetti

Date

10 Jan 2018

This library implements an hybrid system in the form:

\begin{align} \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{align}

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

\begin{align} y = & h(x, u, p) \end{align}

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 the function parameters.
• \( \tau \) 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.