Stability and Performance of Control Systems under Probabilistic Logical Execution Time

The Logical Execution Time (LET) paradigm is a clean abstraction that decouples functional semantics from implementation details in real-time control systems. However, practical experience shows that strictly enforcing LET semantics is often unrealistic: execution on embedded platforms is subject to variability, communication delays, and hardware contention. This makes exact LET adherence costly or even impossible. In this work, we propose to relax the strict deterministic analysis and instead study a probabilistic model that captures the essence of LET implementations without requiring full conformance. By allowing read and write instants to vary within given probability distributions, the probabilistic LET (pLET) framework maintains the conceptual benefits of LET while reflecting the timing uncertainty of real systems. Our analysis uses a probabilistic model for data propagation through a directed acyclic graph (DAG) of periodic tasks. We use the model to quantify the impact of implementation-related considerations on the performance of the closed-loop system. We apply the analysis to an example case study and to a model of a Crazyflie drone, showing that the pLET analysis allows us to give system-level guarantees and can help refine real-time parameters such as task periods.