Weakly Hard Real-Time Model for Control Systems: A Survey

Abstract

The concept of weakly hard real-time systems can be used to model real-time systems that may tolerate occasional deadline misses in a bounded and predictable manner. This model applies to many practical applications and is particularly interesting in the context of real-time control systems. In practice, applying hard real-time constraints may be too rigid since a certain amount of deadline misses is acceptable in some applications. In order to maintain system stability, limitations on the amount and distribution of violated deadlines need to be imposed. These limitations can be formally expressed as weakly hard real-time constraints. Current research in the field of weakly hard real-time task scheduling is focused on designing scheduling algorithms that guarantee the fulfillment of constraints, while aiming to maximize the total number of timely completed task instances. This paper provides an extensive literature review of the work related to the weakly hard real-time system model and its link to the field of control systems design. The weakly hard real-time system model and the corresponding scheduling problem are described. Furthermore, an overview of system models derived from the generalized weakly hard real-time system model is provided, with an emphasis on models that apply to real-time control systems. The state-of-the-art algorithms for scheduling tasks with weakly hard real-time constraints are described and compared. Finally, an overview of controller design methods that rely on the weakly hard real-time model is given.

Keywords: control and scheduling co-design; real-time task scheduling; weakly hard real-time systems.

Figure 1

Example of an autonomous mobile robot (AMR) control system.

Figure 2

System model with $(m,k)$-firm constraints. Modified from [5]. The streams are denoted as ${\tau }_i$, while the j-th request of the i-th stream is denoted as $J_i^j$.

Figure 3

Transition diagram for a task with $\left(\genfrac{}{}{0pt}{}{2}{3}\right)$ constraint. Modified from [5].

Figure 4

System model for the CSA. Modified from [57].

Figure 5

A comparison of EDF, IDBP, and S-CSA with different class numbers. Data taken from [57].

Figure 6

A comparison of PDS obtained by the GDPA, GDPA-S, DBP, and EDF approaches. Data taken from [68].

Figure 7

A comparison of job-skipping algorithms according to QoS metric. Data taken from [73].

Figure 8

A comparison of job-skipping algorithms with respect to the dynamic overhead. Data taken from [73].

Figure 9

A comparison of the number of dynamic failures for DWCS, EDF, and BM scheduling algorithms. Data taken from [81].

Figure 10

Mean rate of met deadlines obtained by the MRA, MAA, and EDF algorithms. Data taken from [82].

Figure 11

An illustration of control loop timing characteristics. (a) Input-output latency and sampling period. (b) Sampling and latency jitter.

Figure 12

An illustration of performance metrics analyzed through the step response: delay time $t_d$, rise time $t_r$, overshoot $M_p$, and settling time $t_s$.

Figure 13

An illustration of the allowed state space.