Moore-Smith theory for uniform spaces through asymptotic equivalence

Moore-Smith theory tells us how to generate a topology by defining convergence of nets rather than using a definition of open set. In this report, we extend this theory to uniform spaces, and show how a uniform space can be generated by defining asymptotic equivalence of nets rather than using a definition of entourage

Hybrid process algebra

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Prefix orders as a general model of dynamics

In this report we formalize and study the notion of prex order on the executions of general dynamical systems and use basic category theory to show that appropriate structure preserving maps between such orders lead to the well-known notions of bisimulation, renement, product, and union of behavior, without relying on a notion of 'next state'. Thus these notions are generalized to apply to arbitrary dynamical systems, including continuous and hybrid systems

Action and predicate safety of hybrid processes

Abstract In this paper, we study two kinds of safety properties for hybrid processes, namely safety for actions and safety for predicates on model variables. We give an algebraic specification of these safety properties using the process algebra HyPA, and show how to reduce the question of safety of a linear process specification to the question of safety of its sub-processes. As an example, we study a variant of Fischer¿s protocol, in which there can be a relative error between the clocks that are used

Towards budgeting in real-time calculus : deferrable servers

Budgeting of resources is an often used solution for guaranteeing performance of lower priority tasks. In this paper, we take a formal approach to the modeling of a deferrable server budgeting strategy, using real-time calculus. We prove a scheduling theorem for deferrable servers, and as a corollary show that an earlier claim of Davis and Burns, that periodic servers dominate deferrable servers with respect to schedulability, no longer holds when the context of the comparison is slightly generalized

Beyond Zeno-behaviour

When modelling and analysing hybrid systems using techniques from computing science we may encounter problems with so-called Zeno-behaviour. This is the phenomenon that an innite number of events accumulates before a nite time (Zeno-time). When this happens the standard techniques from computing science fail to dis-tinguish between events that happen after that sequence of events. Many of those techniques have a semantics based on labelled transi-tion systems. In this article, we concentrate on those transition systems and try to nd a solution for the Zeno-problem. We rst introduce transi-tions over innite sequences, since an innite number of events needs to be described. Then we (re-)dene a notion of convergence over sequences in a metric space. Considering a transition system with a metric state space and transitions labelled by sequences we can dene a notion of prex- and accumulation-closedness. Finally within prex-and accumulation-closed transition systems, bisimilarity turns out to distinguish between various kinds of transnite behaviour. The bounc-ing ball, an example from hybrid system theory, is used to illustrate the relevance of these new denitions. 1

Constitutive hybrid processes

Introduction When modeling a physical system, it is common practice to describe the components that constitute the system, using so-called constitutive relations on the physical variables that play a role in the system. The intersection of all these relations then forms a model of the system as a whole. The behavior of physical systems is usually assumed to be continuous and, therefore, the constitutive relations are often stated as differential algebraic equations. When part of the continuous behavior occurs very fast, however, as is for example the case when studying impact phenomena, it may be convenient to describe this behavior as being discontinuous. The constitutive relations that are used to describe the system, should in that case not only contain algebraic differential equations (for the large time-scale behavior), but using also equations that describe the discontinuous behavior (for the behavior during impact). In this report, we describe the constitutive relations of many more-or-less standard components in physical modeling, using the hybrid process algebra HyPA [4]. This algebra allows us to describe combinations of continuous and discontinuous behavior as one, hybrid, process (hence, the title of this report). As a vehicle for our thoughts, we use a graphical language named bond graphs [11] to formalize our physical models, before engaging in the construction of constitutive relations for them. Bond graphs generalize all domains of physics, such as electronics, hydraulics, and mechanics, in one framework. Recently, they have been extended with elements that are suitable for describing discontinuous behavior [10, 9, 1, 12]. This report, can therefore also be considered an attempt to give a formal semantics to hybrid bond graphs. Our expectation is, that after we have explained how to derive hybrid constitutive processes using hybrid bond graphs, it will also be easier to derive these processes directly, without using bond graphs as an intermediate step. Nevertheless, the construction of a bond graph sometimes gives additional insight in the workings of a system, and can facilitate analysis in many ways (see for example [8, 14, 3, 2]). In general, different model representations have strengths in different kinds of analysis. In the next section, we give a short discussion on the modeling of physical systems through constitutive relations, using an example from mechanical engineering. Then, we briefly explain the traditional bond graph modeling method and discuss the need for abstraction from small timescale behavior. In section 3 we briefly discuss the syntax and semantics of hybrid process algebra [4]. In section 4, we turn back to the bond graph modeling formalism, to see how the constitutive relations of the bond graph elements can be extended to include discontinuous behavior. In the last section, we give modeling examples that show how hybrid bond graph models can be made of several physical systems, and how these bond graph models can be turned into constitutive hybrid processes describing the systems algebraically

Hybrid transition systems

The theory of hybrid systems studies the combination of continuous and discrete behaviour. "V hell discrete software IS combined with mechanical and electrical components, or IS interacting with, for example, chemical processes, an embed-ded system aris(1s in which the interaction between the continuous behaviou