In a typical cyber-physical system (CPS), the cyber/computation subsystem controls the physical subsystem, and therefore the computer society has recently paid considerable attention to CPS research. To keep such a CPS stable, feedback control with periodic computation tasks has been widely used, and its theoretical guarantee of stability has been made with periodic real-time task models that enforce strict periodic control updates. However, some control update misses are usually allowed (e.g., via system over-design) in certain physical subsystem states (PSSes) without causing system instability, and the resources required for strict periodic control updates can thus be reduced or used for other purposes, achieving efficient controls for the entire CPS in terms of the operational cost, such as fuel consumption or tracking accuracy. In this paper, we propose a new periodic, fault-tolerant CPS task model, which not only expresses efficiency and stability of the underlying physical subsystem, but also generalizes existing periodic real-time task models, by capturing a tolerable number of control update misses in different PSSes. To demonstrate the utility of this model, we develop a new scheduling mechanism that prioritizes jobs (i.e., periodic invocations) of a set of tasks not only by the nature of each task, but also by the number of consecutive prior job deadline misses. Based on its analysis in terms of stability and efficiency, we also propose a priority-assignment policy that lowers the system operation cost without compromising stability. Our in-depth analysis and simulation results show that the scheduling mechanism and its analysis, as well as the priorityassignment policy under the proposed model not only generalize the existing periodic real-time task models, but also significantly lower the system operation cost without losing stability.

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