Near optimal rate selection for wireless control systems

Abstract

With the advent of industrial standards such as WirelessHART, 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 article, we address the scheduling-control co-design problem of determining the optimal sampling rates of feedback control loops sharing a WirelessHART 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 WirelessHART networks is challenging since it is nondifferentiable, nonlinear, and not in closed-form. We propose four methods to solve this problem. First, we present a subgradient 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. We study SA method under both constant factor penalty and adaptive penalty. Finally, we formulate rate selection as a differentiable convex optimization problem that provides a quick solution through a convex optimization technique. This is based on a new delay bound that is convex and differentiable, and hence simplifies the optimization problem. We study both the gradient descent method and the interior point method to solve it. We evaluate all methods through simulations based on topologies of a 74-node wireless sensor network testbed. The subgradient method is disposed to incur the longest execution time as well as the highest control cost among all methods. Among the SA-based constant penalty method, the greedy heuristic, and the gradient descent method, the first two represent the opposite ends of the tradeoff between control cost and execution time, while the third one hits the balance between the two. We further observe that the SA based adaptive penalty method is superior to the constant penalty method, and that the interior point method is superior to the gradient method. Thus, the interior point method and the SA-based adaptive penalty method are the two most effective approaches for rate selection. While both methods are competitive against each other in terms of control cost, the interior point method is significantly faster than the penalty method. As a result, the interior point method upon convex relaxation is more suitable for online rate adaptation than the SA based adaptive penalty method due to their significant difference in run-time efficiency.