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In factory automation, heterogeneous manufacturing processes need to becoordinated over wireless networks to achieve safety and efficiency. Thesewireless networks, however, are inherently unreliable due to shadow fadinginduced by the physical motion of the machinery. To assure both safety andefficiency, this paper proposes a state-dependent channel model that capturesthe interaction between the physical and communication systems. By adoptingthis channel model, sufficient conditions on the maximum allowable transmissioninterval are then derived to ensure stochastic safety for a nonlinear physicalsystem controlled over a state-dependent wireless fading channel. Under thesesufficient conditions, the safety and efficiency co-design problem isformulated as a constrained cooperative game, whose equilibria representoptimal control and transmission power policies that minimize a discountedjoint-cost in an infinite horizon. This paper shows that the equilibria of theconstrained game are solutions to a non-convex generalized geometric program,which are approximated by solving two convex programs. The optimality gap isquantified as a function of the size of the approximation region in convexprograms, and asymptotically converges to zero by adopting a branch-boundalgorithm. Simulation results of a networked robotic arm and a forklift truckare presented to verify the proposed co-design method.

Co-design of Safe and Efficient Networked Control Systems in Factory Automation with State-dependent Wireless Fading Channels