Distributed Control of Stochastic Manufacturing Processes Based on Consensus Algorithms

In this paper, we deal with a distributed control of stock levels of buffers in a large-scale manufacturing factory. We suppose that the manufacturing factory is composed of many production processes and transportation processes. Each production process has several input buffers to stock materials for production temporarily and an output buffer to stock the produced materials temporarily. The transportation process is assumed to be realized by a swarm of vehicles, which flexibly move between buffers and transport the materials conveniently. We model the production processes as deterministic dynamical systems and the transportation processes as stochastic events. Then, we propose a distributed control method for the production rates and the transportation probabilities by employing an idea of consensus algorithms and rigorously prove that all the normalized stock levels of the buffers are globally stable at consensus values in a probabilistic sense. We finally demonstrate the effectiveness of our proposed method by numerical simulations.