From dissipativity theory to compositional synthesis of symbolic models
From dissipativity theory to compositional synthesis of symbolic models
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DOI：
10.1109/indiancc.2018.8307949
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发表时间：
2017-10
期刊：
影响因子：
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通讯作者：
Abdalla Swikir;A. Girard;Majid Zamani
中科院分区：
文献类型：
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作者：
Abdalla Swikir;A. Girard;Majid Zamani
在这项工作中，我们引入了一个组合框架，用于构建相互关联的离散时间控制系统的有限抽象（又称符号模型）。该组合方案基于离散时间控制子系统的联合耗散型性质及其有限抽象。在本文的第一部分，我们使用所谓的存储函数作为每个子系统与其有限抽象之间的关系的概念，构造了所谓的交替仿真函数作为相互连接的有限抽象与控制系统之间的关系的概念。导出的交替模拟函数用于量化整体互联混凝土系统的输出行为与其有限抽象的输出行为之间的误差。在论文的第二部分，我们提出了一类具有增量无源性的离散时间控制系统的有限抽象及其相应的存储函数的构造方法。我们证明了如果一个离散时间控制系统是所谓的增量无源的，那么我们可以通过适当的输入和状态集的量化以及相应的存储函数来构造它的有限抽象。最后，在不限制增益或子系统数量的情况下，以组合方式构造线性离散控制系统网络及其相应的交替仿真函数的有限抽象来说明所提出的结果。
In this work, we introduce a compositional framework for the construction of finite abstractions (a.k.a. symbolic models) of interconnected discrete-time control systems. The compositional scheme is based on the joint dissipativity-type properties of discrete-time control subsystems and their finite abstractions. In the first part of the paper, we use a notion of so-called storage function as a relation between each subsystem and its finite abstraction to construct compositionally a notion of so-called alternating simulation function as a relation between interconnected finite abstractions and that of control systems. The derived alternating simulation function is used to quantify the error between the output behavior of the overall interconnected concrete system and that of its finite abstraction. In the second part of the paper, we propose a technique to construct finite abstractions together with their corresponding storage functions for a class of discrete-time control systems under some incremental passivity property. We show that if a discrete-time control system is so-called incrementally passivable, then one can construct its finite abstraction by a suitable quantization of the input and state sets together with the corresponding storage function. Finally, the proposed results are illustrated by constructing a finite abstraction of a network of linear discrete-time control systems and its corresponding alternating simulation function in a compositional way without imposing any restriction on the gains or the number of the subsystems.