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Symbolic models for incrementally stable switched systems with aperiodic time sampling ?

机译:具有非周期性时间采样的渐进稳定切换系统的符号模型

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In this paper, we consider the problem of symbolic model design for the class of incrementally stable switched systems. Contrarily to the existing results in the literature where switching is considered as periodically controlled, in this paper, we consider aperiodic time sampling resulting either from uncertain or event-based sampling mechanisms. Firstly, we establish sufficient conditions ensuring that usual symbolic models computed using periodic time-sampling remain approximately bisimilar to a switched system when the sampling period is uncertain and belongs to a given interval; estimates on the bounds of the interval are provided. Secondly, we propose a new method to compute symbolic models related by feedback refinement relations to incrementally stable switched systems, using an event-based approximation scheme. For a given precision, these event-based models are guaranteed to enable transitions of shorter duration and are likely to allow for more reactiveness in controller design. Finally, an example is proposed in order to illustrate the proposed results and simulations are performed for a Boost dc-dc converter structure.
机译:在本文中,我们考虑了一类增量稳定切换系统的符号模型设计问题。与文献中将开关视为周期性控制的现有结果相反,在本文中,我们考虑了由不确定或基于事件的采样机制导致的非周期性时间采样。首先,我们建立了充分的条件,以确保在采样周期不确定且属于给定间隔时,使用定期时间采样计算的常用符号模型与切换系统保持近似双相似。提供了区间范围的估计。其次,我们提出了一种新的方法,该方法使用基于事件的近似方案来计算与反馈稳定关系相关的符号模型,该反馈模型关系到增量稳定的切换系统。对于给定的精度,这些基于事件的模型可以保证实现更短持续时间的转换,并且可能允许控制器设计具有更大的反应性。最后,提出一个示例以说明所提出的结果,并对Boost dc-dc转换器结构进行仿真。

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