Efficient Scheduler Synthesis For Periodic Event Triggered Control Systems

Abstract

In recent years, Networked Control Systems (NCS) have become more popular, partly because of the increasing accessibility. In NCS, multiple plants and controllers are connected over a wired or wireless shared network, possibly having significant spatial separation. A major issue that arises is network congestion: If too many control loops are connected to the network, the shared communication channels become oversaturated, causing the packages to be lost, and subsequently the individual control loops might become unstable. One solution to this problem is to make use of Periodic Event Triggered Control (PETC), where a triggering condition is checked periodically, and if this condition is satisfied, the control loop is closed. Control using PETC becomes inherently aperiodic, as opposed to the periodic nature of standard control implementations. This aperiodicity introduces another issue: Avoiding collision of communication events caused by the triggering of control loops. To resolve this issue, schedulers have to be designed for the control loops. There are approaches already available that can automatically synthesize schedulers for a collection of PETC systems. However, these share a common issue in that these scale poorly with the number of subsystems. This thesis explores new algorithms for synthesization of schedulers for PETC systems, with the goal of better scalability. This is done by first abstracting the triggering behaviour of the individual control loops and representing these by Transition Systems (TSs). Then schedulers are synthesized by solving a safety game. To increase efficiency of the safety game, several states are combined by partitioning. Additionally, a major boost in performance is gained by representing the TSs by Binary Decision Diagrams (BDDs). Finally, a method to increase schedulability is also investigated by allowing the control loops to occasionally trigger late.