Control theory allows one to design controllers that are robust to external disturbances, model simplification, and modelling inaccuracy. Researchers have investigated whether the robustness carries on to the controller’s digital implementation, mostly looking at how the controller reacts to either communication or computational problems. Communication problems are typically modelled using random variables (i.e., estimating the probability that a fault will occur during a transmission), while computational problems are modelled using deterministic guarantees on the number of deadlines that the control task has to meet. These fault models allow the engineer to both design robust controllers and assess the controllers’ behaviour in the presence of isolated faults. Despite being very relevant for the real-world implementations of control system, the question of what happens when these faults occur simultaneously does not yet have a proper answer. In this paper, we answer this question in the stochastic setting, using the theory of Markov Jump Linear Systems to provide stability contracts with almost sure guarantees of convergence. For linear time-invariant Markov jump linear systems, mean square stability implies almost sure convergence – a property that is central to our investigation. Our research primarily emphasises the validation of this property for closed-loop systems that are subject to packet losses and computational overruns, potentially occurring simultaneously. We apply our method to two case studies from the recent literature and show their robustness to a comprehensive set of faults. We employ closed-loop system simulations to empirically derive performance metrics that elucidate the quality of the controller implementation, such as the system settling time and the integral absolute error.

The policy used to implement a control algorithm in a real-time system can significantly affect the quality of control. In this paper, we present a method to adapt the controller implementation, with the objective to improve the system’s performance under real-time faults. Our method compensates for missing state updates by adapting the controller parameters according to the number of consecutively missed deadlines. It extends the state-of-the-art by considering dynamic controllers, which have had limited coverage in previous literature. The adaptation mechanism can be precomputed offline, solely based on knowledge about the controller and not on the controlled plant. The approach is indifferent to the control design, as well as to the scheduling policy, and can be automatically realised by the operating system, thus improving the robustness of the control system to intermittent and unexpected real-time faults. We develop a stochastic performance analysis method and apply it to both a real plant and numerous simulated plants to evaluate our adaptive controller. Complementary to the stochastic analysis, we also do worst-case stability analysis of the resulting system. The results confirm the conjuncture that the adaptive controller improves both the performance and robustness in the presence of deadline misses.

Weakly-hard models have been used to analyse real-time systems subject to patterns of deadline hits and misses. However, the tools that are available in the literature have a set of shortcomings. The analysis they offer is limited to a single weaklyhard constraint and to patterns that specify the number of misses, rather than the number of hits. Furthermore, the scalability of the tools is limited, effectively making it hard to address systems where deadline misses are really sporadic events. In this paper we present WeaklyHard.jl, a scalable tool to analyse a set of weakly hard constraints belonging to all the four types of weakly hard models. To achieve scalability, we exploit novel dominance relations between weakly-hard constraints, based on deadline hits. We provide experimental evidence of the tool’s scalability, compared to the state-of-the-art for a single constraint, a thorough investigation of hit-based weakly-hard constraints, and a sensitivity analysis to constraint set parameters.

Control systems are by design robust to various disturbances, ranging from noise to unmodelled dynamics. Recent work on the weakly hard model - applied to controllers - has shown that control tasks can also be inherently robust to deadline misses. However, existing exact analyses are limited to the stability of the closed-loop system. In this paper we show that stability is important but cannot be the only factor to determine whether the behaviour of a system is acceptable also under deadline misses. We focus on systems that experience bursts of deadline misses and on their recovery to normal operation. We apply the resulting comprehensive analysis (that includes both stability and performance) to a Furuta pendulum, comparing simulated data and data obtained with the real plant. We further evaluate our analysis using a benchmark set composed of 133 systems, which is considered representative of industrial control plants. Our results show the handling of the control signal is an extremely important factor in the performance degradation that the controller experiences - a clear indication that only a stability test does not give enough indication about the robustness to deadline misses.