From dissipativity theory to compositional synthesis of symbolic models

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01620525
Contributeur : Antoine Girard <>
Soumis le : vendredi 20 octobre 2017 - 16:29:26
Dernière modification le : mercredi 21 novembre 2018 - 16:44:40

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Abdalla Swikir, Majid Zamani, Antoine Girard. From dissipativity theory to compositional synthesis of symbolic models. Indian Control Conference, Jan 2018, Kanpur, India. 〈10.1109/indiancc.2018.8307949 〉. 〈hal-01620525〉

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