Wireless Control Network: A New Approach for Control over Networks

We present a method to stabilize a plant with a network of resource constrained wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach treats the network itself as the controller. Specifically, we formulate a strategy for each node in the network to follow, where at each time-step, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. We show that this causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We call this architecture a Wireless Control Network (WCN), and show that it introduces very low computational and communication overhead to the nodes in the network, allows the use of simple transmission scheduling algorithms, and enables compositional design (where the existing wireless control infrastructure can be easily extended to handle new plants that are brought online in the vicinity of the network).

We provide a numerical design procedure to determine appropriate linear combinations that guarantee closed-loop stability of the system. We also show how the procedure can be modified to provide robustness to node and link failures. We address the problem of WCN synthesis with guaranteed optimal performance of the plant, with respect to standard cost functions. In addition, we characterize fundamental topological conditions to allow stabilization using such a scheme. To achieve this, we exploit the fact that the WCN scheme causes the network to act as a linear dynamical system, and analyze the coupling between the plant's dynamics and the dynamics of the network. We show that the derived condition is analogous to the typical min-cut condition required in classical information dissemination problems. Furthermore, we specify equivalent topological conditions for stabilization over a wired (or point-to point) network that employs network coding in a traditional way - as a communication mechanism between the plant's sensors and decentralized controllers located at the actuators. Finally, we demonstrate how the WCN can be used on a practical, industrial case study.