Control of continuous and hybrid systems using discrete abstractions often suffers from scalability issues, due to the use of state space partitions as symbolic states. In this paper, for incrementally stable switched systems, we introduce a class of abstractions that do not rely on state space partitions but use mode sequences as symbolic states. Our approach differs from existing works by the possibility of considering sequences of varying length, giving the possibility to adjust locally the resolution of the abstraction. Temporal constraints on the switching signal can also be taken into account. We thus define multi-resolution bisimilar abstractions that enjoy interesting properties that can be used to design specific algorithms to synthesize safety controllers. These algorithms need not compute the full abstraction that is built incrementally during controller synthesis, exploring finer resolutions only when the specification cannot be enforced at the coarser level. We illustrate the approach by a numerical example inspired by road traffic regulation.

中文翻译：

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使用无离散化多分辨率抽象的增量稳定切换系统的安全综合

由于使用状态空间分区作为符号状态，使用离散抽象控制连续和混合系统通常会遇到可扩展性问题。在本文中，对于增量稳定的切换系统，我们引入了一类不依赖于状态空间分区而是使用模式序列作为符号状态的抽象。我们的方法与现有作品的不同之处在于，可以考虑不同长度的序列，从而可以局部调整抽象的分辨率。也可以考虑对开关信号的时间限制。因此，我们定义了多分辨率双相似抽象，这些抽象具有有趣的特性，可用于设计特定算法以合成安全控制器。这些算法不需要计算在控制器综合过程中增量构建的完整抽象，仅当规范无法在较粗略的级别强制执行时才探索更精细的分辨率。我们通过一个受道路交通管制启发的数值例子来说明该方法。