Optimal Priority Assignment to Control Tasks

In embedded real-time systems, task priorities are often assigned to meet deadlines. However, in control tasks, a late completion of a task has no catastrophic consequence; rather, it has a quantifiable impact in the control performance achieved by the task. In this article, we address the problem of determining the optimal assignment of priorities and periods of sampled-data control tasks that run over a shared computation unit. We show that the minimization of the overall cost can be performed efficiently using a branch and bound algorithm that can be further speeded up by allowing for a small degree of suboptimality. Detailed numerical simulations are presented to show the advantages of various branching alternatives, the overall algorithm effectiveness, and its scalability with the number of tasks.