Near optimal rate selection for wireless control systems

With the advent of industrial standards such as Wireless Hart, process industries are now gravitating towards wireless control systems. Due to limited bandwidth in a wireless network shared by multiple control loops, it is critical to optimize the overall control performance. In this paper, we address the scheduling-control co-design problem of determining the optimal sampling rates of feedback control loops sharing a Wireless Hart network. The objective is to minimize the overall control cost while ensuring that all data flows meet their end-to-end deadlines. The resulting constrained optimization based on existing delay bounds for Wireless Hart networks is challenging since it is non-differentiable, non-linear, and not in closed-form. We propose four methods to solve this problem. First, we present a sub gradient method for rate selection. Second, we propose a greedy heuristic that usually achieves low control cost while significantly reducing the execution time. Third, we propose a global constrained optimization algorithm using a simulated annealing (SA) based penalty method. Finally, we formulate rate selection as a differentiable convex optimization problem that provides a closed-form solution through a gradient descent method. This is based on a new delay bound that is convex and differentiable, and hence simplifies the optimization problem. We evaluate all methods through simulations based on topologies of a 74-node wireless sensor network testbed. Surprisingly, the sub gradient method is disposed to incur the longest execution time as well as the highest control cost among all methods. SA and the greedy heuristic represent the opposite ends of the trade off between control cost and execution time, while the gradient descent method hits the balance between the two.