The Wireless Control Network: A New Approach for Control Over Networks

Abstract

Abstract-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 provide a numerical design procedure to determine appropriate linear combinations to be applied by each node so that the transmissions of the nodes closest to the actuators will stabilize the plant. We also show how our design procedure can be modified to maintain mean square stability under packet drops in the network, and present a distributed scheme that can handle node failures while preserving stability. We call this architecture a Wireless Control Network, 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).

Topological Conditions for In-Network Stabilization of Dynamical Systems

“…Motivated by the above issues, in a recent paper [7] we asked the following question: is it possible to do away with the standard "sensor → channel → controller/estimator → channel → actuator" architecture ( Fig. 1(a)) and have the computation of the control law be performed in-network?…”

“…In [7], we proposed a method for distributed in-network computation of a stabilizing input sequence. The WCN scheme requires that each wireless node maintains a scalar 2 state and implements a simple, lightweight linear iterative procedure.…”

“…The original WCN scheme from [7] requires each plant input u i [k], i ∈ {1, 2, ..., m}, to be a linear combination of values from the nodes in actuator a i 's neighborhood. In this work we generalize this and allow each actuator a i , (i ∈ {1, 2, ..., m}) to maintain a (possibly) vector state 4 denoted by…”

“…This is a nonconvex problem (and hence difficult to solve in general), but various numerical procedures have been proposed in the literature (e.g., [26], [27]). In [7], we adapted some of these numerical procedures to find values for the nonzero WCN parameters so that the closed-loop system is stable, given a network topology and a predefined state size maintained by each node. In addition, a procedure similar to the ones from [7], [8] can be used to extract a stabilizing configuration 5 for the closed-loop system with unreliable communication links.…”

“…In [7], we adapted some of these numerical procedures to find values for the nonzero WCN parameters so that the closed-loop system is stable, given a network topology and a predefined state size maintained by each node. In addition, a procedure similar to the ones from [7], [8] can be used to extract a stabilizing configuration 5 for the closed-loop system with unreliable communication links. 6 However, the proposed procedure is iterative in nature, and convergence depends on the initialization point for the algorithm.…”