Safety-Aware Flexible Schedule Synthesis for Cyber-Physical Systems Using Weakly-Hard Constraints

With the emergence of complex autonomous systems, multiple control tasks are increasingly being implemented on shared computational platforms. Due to the resource-constrained nature of such platforms in domains such as automotive, scheduling all the control tasks in a timely manner is often difficult. The usual requirement---that all task invocations must meet their deadlines---stems from the isolated design of a control strategy and its implementation (including scheduling) in software. This separation of concerns, where the control designer sets the deadlines, and the embedded software engineer aims to meet them, eases the design and verification process. However, it is not flexible and is overly conservative. In this paper, we show how to capture the deadline miss patterns under which the safety properties of the controllers will still be satisfied. The allowed patterns of such deadline misses may be captured using what are referred to as "weakly-hard constraints." But scheduling tasks under these weakly-hard constraints is non-trivial since common scheduling policies like fixed-priority or earliest deadline first do not satisfy them in general. The main contribution of this paper is to automatically synthesize schedules from the safety properties of controllers. Using real examples, we demonstrate the effectiveness of this strategy and illustrate that traditional notions of schedulability, e.g., utility ratios, are not applicable when scheduling controllers to satisfy safety properties.