Stability Verification of Self-Timed Control Systems Using Model-Checking

Cyber-physical control systems are typically time-triggered because the Analog to Digital (A/D) and Digital to Analog (D/A) converters are triggered by a periodic clock. This enables analytical stability analysis of closed-loop models in case the plant and controller are linear. However ensuring periodic sampling requires that a sampling period is selected larger than the Worst-Case Execution Times (WCETs) of the digital control tasks. Unfortunately, low sampling rates must be selected as a result of loose WCET bounds especially if multi-processor hardware is applied with shared data caches and SDRAM memory. In this paper we propose a model-checking based stability analysis approach for control systems that sample aperiodically. Our approach is targetting self-timed systems, where the A/D and D/A converters are driven by internal events, such as the completion of a task, which also trigger subsequent task executions. During self-timed execution the average sampling period tends to be significantly smaller than possible in time-triggered mode, and as a result the control performance is improved significantly. Self-timed systems also allow the use of a running average workload characterization of the tasks which is tighter than a WCET characterization, and which can greatly improve the accuracy of the stability analysis results. We show using two self-timed control systems that control performance in terms of stability and settling time improves for self-timed systems when the running average workload characterization is applied. Furthermore, we point at an essential feature that is needed for asymptotic stability analysis which is missing in well known model checkers such as SpaceEx.