  We consider the problem of optimal multi-modes switching in finite horizon,
when the state of the system, including the switching cost functions are
arbitrary ($g_{ij}(t,x)\geq 0$). We show existence of the optimal strategy, and
give when the optimal strategy is finite via a verification theorem. Finally,
when the state of the system is a markov process, we show that the vector of
value functions of the optimal problem is the unique viscosity solution to the
system of $m$ variational partial differential inequalities with
inter-connected obstacles.
