  In factory automation, heterogeneous manufacturing processes need to be
coordinated over wireless networks to achieve safety and efficiency. These
wireless networks, however, are inherently unreliable due to shadow fading
induced by the physical motion of the machinery. To assure both safety and
efficiency, this paper proposes a state-dependent channel model that captures
the interaction between the physical and communication systems. By adopting
this channel model, sufficient conditions on the maximum allowable transmission
interval are then derived to ensure stochastic safety for a nonlinear physical
system controlled over a state-dependent wireless fading channel. Under these
sufficient conditions, the safety and efficiency co-design problem is
formulated as a constrained cooperative game, whose equilibria represent
optimal control and transmission power policies that minimize a discounted
joint-cost in an infinite horizon. This paper shows that the equilibria of the
constrained game are solutions to a non-convex generalized geometric program,
which are approximated by solving two convex programs. The optimality gap is
quantified as a function of the size of the approximation region in convex
programs, and asymptotically converges to zero by adopting a branch-bound
algorithm. Simulation results of a networked robotic arm and a forklift truck
are presented to verify the proposed co-design method.
