Stability is a fundamental requirement of dynamical systems. Most of the works concentrate on verifying stability for a given stability region. In this paper we tackle the problem of synthesizing P -stable abstractions. Intuitively, the P -stable abstraction of an open dynamical system characterizes the transitions between stability regions in response to external inputs. The stability regions are not given - rather, they are synthesized as the tightest representation with respect to a given set of relevant predicates P . A P -stable abstraction is enriched by timing information derived from the duration of stabilization. We implement a synthesis algorithm in the framework of Abstract Interpretation, that allows different degrees of approximation. We show the representational power of P -stable abstractions, that provide a high-level account of the behavior of the system with respect to stability, and we experimentally evaluate the effectiveness of a compositional approach, that allows synthesizing P -stable abstractions for significant systems.

Synthesis of P-Stable Abstractions

Becchi, Anna;Cimatti, Alessandro;
2020

Abstract

Stability is a fundamental requirement of dynamical systems. Most of the works concentrate on verifying stability for a given stability region. In this paper we tackle the problem of synthesizing P -stable abstractions. Intuitively, the P -stable abstraction of an open dynamical system characterizes the transitions between stability regions in response to external inputs. The stability regions are not given - rather, they are synthesized as the tightest representation with respect to a given set of relevant predicates P . A P -stable abstraction is enriched by timing information derived from the duration of stabilization. We implement a synthesis algorithm in the framework of Abstract Interpretation, that allows different degrees of approximation. We show the representational power of P -stable abstractions, that provide a high-level account of the behavior of the system with respect to stability, and we experimentally evaluate the effectiveness of a compositional approach, that allows synthesizing P -stable abstractions for significant systems.
978-3-030-58767-3
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11582/325719
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