On Modeling, Complexities, and Automatic Configuration of Wireless Industrial Control Networks

We propose a mathematical model for wireless industrial control systems and analyze the engineering challenge of co-scheduling networking and control in this context. We demonstrate the use of the model using a small case study and explain how our modelling approach allows for self-configuring and self-adapting systems. The main theoretical contribution of the paper is a mathematical formulation of the computational problem of synthesizing a co-design of scheduling and control for wireless industrial control systems and a mathematical proof that this problem is computationally hard. We also identify relevant special network topologies for which the problem can be efficiently solved.