Symbolic models for nonlinear control systems using approximate bisimulation
Symbolic models for nonlinear control systems using approximate bisimulation
复制标题
使用近似互模拟的非线性控制系统的符号模型
DOI：
10.1109/cdc.2007.4434911
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
P. Tabuada
中科院分区：
文献类型：
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作者：
G. Pola;A. Girard;P. Tabuada
控制系统通常由描述物理现象如何受到某些控制参数或输入影响的微分方程建模。虽然这些模型在处理物理现象时非常强大，但它们不太适合描述与物理世界接口的软件和硬件。这激发了最近的兴趣，通过符号模型描述控制系统的连续动态的抽象描述，其中每个“符号”对应于连续模型中的连续状态的“聚合”。由于这些符号模型与计算机科学中用于描述软件和硬件的模型具有相同的性质，因此它们提供了一种统一的语言来研究软件和硬件与物理世界相互作用的控制问题。在本文中，我们证明了每一个增量全局渐近稳定的非线性控制系统是近似等价（双相似）的符号模型的精度，可以选择先验。我们还表明，对于数字控制系统，其中输入是分段常数，并在更强的假设下，增量输入状态稳定，符号模型可以得到，基于一个适当的量化的输入。
Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. This has spurred a recent interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each "symbol" corresponds to an "aggregate" of continuous states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provided a unified language to study problems of control in which software and hardware interact with the physical world. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to symbolic model with a precision that can be chosen a-priori. We also show that for digital controlled systems, in which inputs are piecewise-constant, and under the stronger assumption of incremental input-to-state stability, the symbolic models can be obtained, based on a suitable quantization of the inputs.