arXiv subjects

Anne-Kathrin Schmuck

Publications and source records attributed to Anne-Kathrin Schmuck.

40 records · Page 3Linked to original sources

arXiv2015

Comparing Asynchronous $l$-Complete Approximations and Quotient Based Abstractions

This paper is concerned with a detailed comparison of two different abstraction techniques for the construction of finite state symbolic models for controller synthesis of hybrid systems. Namely, we compare quotient based abstractions (QBA), with different realizations of strongest (asynchronous) $l$-complete approximations (SAlCA) Even though the idea behind their construction is very similar, we show that they are generally incomparable both in terms of behavioral inclusion and similarity relations. We therefore derive necessary and sufficient conditions for QBA to coincide with particular realizations of SAlCA. Depending on the original system, either QBA or SAlCA can be a tighter abstraction.

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arXiv2014

Constructing (Bi)Similar Finite State Abstractions using Asynchronous $l$-Complete Approximations

This paper constructs a finite state abstraction of a possibly continuous-time and infinite state model in two steps. First, a finite external signal space is added, generating a so called $Φ$-dynamical system. Secondly, the strongest asynchronous $l$-complete approximation of the external dynamics is constructed. As our main results, we show that (i) the abstraction simulates the original system, and (ii) bisimilarity between the original system and its abstraction holds, if and only if the original system is $l$-complete and its state space satisfies an additional property.

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arXiv2014

Asynchronous $l$-Complete Approximations

This paper extends the $l$-complete approximation method developed for time invariant systems to a larger system class, ensuring that the resulting approximation can be realized by a finite state machine. To derive the new abstraction method, called asynchronous $l$-complete approximation, an asynchronous version of the well-known concepts of state property, memory span and $l$-completeness is introduced, extending the behavioral systems theory in a consistent way.

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arXiv2014

Simulation and Bisimulation over Multiple Time Scales in a Behavioral Setting

This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and verification of large scale systems. For this new system model different notions of simulation and bisimulation are derived, ensuring that they are, respectively, preorders and equivalence relations for the system class under consideration. These relations can capture a wide selection of similarity notions available in the literature. This paper therefore provides a suitable framework for their comparison

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