On the Joint Design of the Controller, its Placement, and the Routing for Networked Control Systems

When considering networked control systems, the controller is often designed for given loss and delay. However, when the packets are transmitted over a communication network, then the loss and delay between sensor, controller, and actuator depend on the position of the controller and the routes between sensor, controller, and actuator. Since many positions and routes might be possible, the interesting question is: Which controller position and which route gives the best control performance? To answer this question, we first present a model of the communication network and then formulate the controller design, its placement, and the routing as one optimization problem with integer constraints. With the help of two examples, we observe that the optimal route is in general not the one with the shortest delay, highest arrival probability, or minimal number of hops. Moreover, these examples also show that the optimal position of the controller is not always the actuator node.