Abstract
Factors like data dropout, failures of calculation nodes and tasks preemption may cause execution failures of standard sample-and-control at some sampling instants. Such a phenomenon of controller failure is called the control input missing. It has recently worthed a special attention since we have to design a compensation controller in order to generate control inputs when a control input missing occurs. In this chapter, we proposed a new switched hold-zero (HZ) control strategy. When a control input missing occurs, the switched HZ control strategy has two candidate control laws: the hold control and the zero control. In the sequel, we study how to make the optimal switching between the two control laws, by setting an appropriate switching parameter, such that the switched HZ control admits the maximum admissible control input missing rate (ACIMR). With the optimal switching parameter, the switched HZ control strategy is shown to be superior than both the zero-control and the hold-control ones. In addition, we propose an application of the ACIMR: designing an appropriate hyper-sampling period based on the obtained ACIMR. According to the obtained hyper-sampling period, the system may positively discard some sample-and-control executions during the run-time. In this way, we may positively reduce the system resource utilization.
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Notes
- 1.
The definition of the ACIMR will be given later in this chapter.
- 2.
For some chosen Lyapunov function \(V: \mathbb{R}^{n} \mapsto\mathbb{R}\), V(t k )=x′(t k )Px(t k ), where t k denote the sampling instants, if V(t k+1)≤ρV(t k ), ρ>0, the scalar ρ is called a variation rate of the Lyapunov function.
- 3.
Algorithm 13.1 is a one-dimensional problem, which can be easily solved by the LMI toolbox in MATLAB.
- 4.
In fact, we have 45 (computed as the number of 2-combinations from a set of 10 elements) possible forms of the hyper-sampling period if we “discard” 2 samplings in every 10 samplings.
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Çela, A., Ben Gaid, M., Li, XG., Niculescu, SI. (2014). A Switched Hold-Zero Compensation Strategy for DCESs Subject to Control Input Missings. In: Optimal Design of Distributed Control and Embedded Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-02729-6_13
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DOI: https://doi.org/10.1007/978-3-319-02729-6_13
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