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 comparisonComment: Submitted to 22nd Mediterranean Conference on Control and Automatio

Constructing (Bi)Similar Finite State Abstractions using Asynchronous ll-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 $\Phi$-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

Comparing Asynchronous ll-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

Exploiting the Superposition Property of Wireless Communication for Max-Consensus Problems in Multi-Agent Systems

This paper presents a consensus protocol that achieves max-consensus in multi-agent systems over wireless channels. Interference, a feature of the wireless channel, is exploited: each agent receives a superposition of broadcast data, rather than individual values. With this information, the system endowed with the proposed consensus protocol reaches max-consensus in a finite number of steps. A comparison with traditional approaches shows that the proposed consensus protocol achieves a faster convergence.Comment: Submitted for IFAC Workshop on Distributed Estimation and Control in Networked System

Optimalsteuerung zeitbehafteter Synchronisationsgraphen mit Ressourcenkonkurrenz und Aktualisierung von Referenzsignalen

Timed event graphs (TEGs) are a subclass of timed Petri nets that model synchronization and delay phenomena, but not conflict or choice. We consider a scenario where a number of TEGs share one or several resources and are subject to changes in their output-reference signals. Because of resource sharing, the resulting overall discrete event system is not a TEG. We propose a formal method to determine the optimal control input for such systems, where optimality is in the sense of the widely adopted just-in-time criterion. Our approach is based on a prespecified priority policy for the TEG components of the overall system. It builds on existing control theory for TEGs, which exploits the fact that, in a suitable mathematical framework (idempotent semirings such as the max-plus or the min-plus algebra), the temporal evolution of TEGs can be described by a set of linear time-invariant equations.Zeitbehaftete Synchronisationsgraphen (ZSGen) bilden eine spezielle Klasse zeitbehafteteter Petri-Netze. Sie können Synchronisations- und Verzögerungsphänomene modellieren, nicht aber Konflikte. Wir untersuchen ein Szenario, in dem sich mehrere ZSGen eine oder mehrere Ressourcen teilen und die Referenzsignale der ZSGen unvorhersehbaren Änderungen unterworfen sind. Da die beteiligten ZSGen um Ressourcen konkurrieren, ist das Gesamtsystem kein ZSG. Wir beschreiben eine formale Vorgehensweise zur Bestimmung des im just-in-time Sinne optimalen Stellsignals für dieses Gesamtsystem. Unser Ansatz basiert auf einer vorab festgelegten Priorisierung der einzelnen ZSGen. Er baut auf der existierenden Regelungstheorie für ZSGen auf und nutzt die Tatsache, dass sich die zeitliche Entwicklung von ZSGen in einem geeigneten mathematischen Rahmen (idempotente Halbringe wie beispielsweise die max-plus- oder die min-plus-Algebra) durch lineare zeitinvariante Gleichungen beschreiben lässt