A Formal Approach towards Safe and Stable Schedule Synthesis in Weakly Hard Control Systems

Article Type

Research Article

Publication Title

ACM Transactions on Embedded Computing Systems

Abstract

Real-time scheduling of multiple control tasks in a weakly hard setting is an emerging research direction, as it offers a more flexible and feasible environment for task scheduling. This is especially pertinent for resource-constrained embedded applications where tasks are allowed to miss a few deadlines for prudent sharing of computational resources. However, a control task missing its deadline could result in the system being unsafe or unstable. A significant amount of research efforts have been reported in the literature addressing the schedulability of control tasks while preserving the stability or safety. However, all of them focus on a stable schedule or a safe schedule, but not both the safety and stability aspects together. In this work, we ensure both control stability and control safety to generate a safe and stable schedule for a weakly hard task system. In particular, we gradually endorse stability, safety, and schedulability, where we first synthesize a weakly hard constraint that preserves the desired stability of each control task. Next, we correlate stability with control safety and establish some mathematical results that guarantee control safety for an unbounded time horizon, unlike the existing methods. Finally, by leveraging Satisfiability Modulo Theories (SMT), we synthesize the schedule that ensures control stability and safety while minimizing the worst-case response time of all the tasks, in a time-efficient way. To our knowledge, this is the first work to address stability, safety, and schedulability together for weakly hard control task systems. We validate our method through extensive experiments using standard automotive benchmarks. In addition, we demonstrate the efficiency of the proposed method in comparison with some of the state-of-the-art techniques, as well as highlight its scalability, thereby establishing its applicability in real-world scenarios.

DOI

10.1145/3760528

Publication Date

10-1-2025

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