458 research outputs found
Abstractions of Stochastic Hybrid Systems
In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes.
The main result is that this stochastic bisimulation is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same
kind of bisimulation for their continuous parts and respectively for their jumping structures
Equivalence of switching linear systems by bisimulation
A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and input–output equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied.\ud
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Equivalence of hybrid dynamical systems
A common theme in theoretical computer science (in particular, the theory of distributed processes and computer-aided verification) and in systems and control theory is to charac-terize systems which are ‘externally equivalent’. The intuitive idea is that we only want to distinguish between two systems if the distinction can be detected by an external syste
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
Bisimulation theory for switching linear systems
A general notion of hybrid bisimulation is proposed and related to the notions of algebraic, state-space and input-output equivalences for the class of switching linear systems. An algebraic characterization of hybrid bisimulations and a procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Bisimulation-based reduction and simulation-based abstraction are defined and characterized. Connections with observability are investigated
Achievable bisimilar behaviour of abstract state systems
Given a plant system and a desired system, we study conditions for which there exists a controller that interconnected with the plant, yields a system that is bisimilar to the desired system. Some sufficient and some necessary conditions are provided in the general case of (non-deterministic) abstract state systems and stronger results are obtained for the special classes of autonomous abstract state systems, finite abstract state systems, and non-deterministic linear dynamical systems
Behavioural hybrid process calculus
Process algebra is a theoretical framework for the modelling and analysis of the behaviour of concurrent discrete event systems that has been developed within computer science in past quarter century. It has generated a deeper nderstanding of the nature of concepts such as observable behaviour in the presence of nondeterminism, system composition by interconnection of concurrent component systems, and notions of behavioural equivalence of such systems. It has contributed fundamental concepts such as bisimulation, and has been successfully used in a wide range of problems and practical applications in concurrent systems. We believe that the basic tenets of process algebra are highly compatible with the behavioural approach to dynamical systems. In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems. It provides a natural framework for the concurrent composition of such systems, and can deal with nondeterministic behaviour that may arise from the occurrence of internal switching events. Standard process algebraic techniques lead to the characterisation of the observable behaviour of such systems as equivalence classes under some suitably adapted notion of bisimulation
Constructing (Bi)Similar Finite State Abstractions using Asynchronous -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 -dynamical system.
Secondly, the strongest asynchronous -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
-complete and its state space satisfies an additional property
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