  This paper presents a linear programming approach for the optimal control of
nonlinear switched systems where the control is the switching sequence. This is
done by introducing modal occupation measures, which allow to relax the problem
as a primal linear programming (LP) problem. Its dual linear program of
Hamilton-Jacobi-Bellman inequalities is also characterized. The LPs are then
solved numerically with a converging hierarchy of primal-dual
moment-sum-of-squares (SOS) linear matrix inequalities (LMI). Because of the
special structure of switched systems, we obtain a much more efficient method
than could be achieved by applying standard moment/SOS LMI hierarchies for
general optimal control problems.
