  In this paper, we consider the problem of controlling a dynamical system such
that its trajectories satisfy a temporal logic property in a given amount of
time. We focus on multi-affine systems and specifications given as
syntactically co-safe linear temporal logic formulas over rectangular regions
in the state space. The proposed algorithm is based on the estimation of time
bounds for facet reachability problems and solving a time optimal reachability
problem on the product between a weighted transition system and an automaton
that enforces the satisfaction of the specification. A random optimization
algorithm is used to iteratively improve the solution.
