  Peak estimation of hybrid systems aims to upper bound extreme values of a
state function along trajectories, where this state function could be different
in each subsystem. This finite-dimensional but nonconvex problem may be lifted
into an infinite-dimensional linear program (LP) in occupation measures with an
equal objective under mild finiteness/compactness and smoothness assumptions.
This LP may in turn be approximated by a convergent sequence of upper bounds
attained from solutions of Linear Matrix Inequalities (LMIs) using the
Moment-Sum-of-Squares hierarchy. The peak estimation problem is extended to
problems with uncertainty and safety settings, such as measuring the distance
of closest approach between points along hybrid system trajectories and unsafe
sets.
