Abstract

In this paper, we present an object-oriented approach to the design of hybrid systems using UMLh, a variant of UML for hybrid systems. We introduce the main concepts of UMLh, describe a support tool, and look at their application for the design of a steam-boiler system.

1.1 INTRODUCTION

Hybrid systems are networks of components with discrete and continuous behavior. Typical examples of hybrid systems are physical processes along with their discrete controllers. As such systems are often involved in safety-critical applications, their analysis plays an important role in current research. Three major analysis strategies can be identified: verification, testing, and simulation. Recently, numerous formalisms have been developed for the precise specification of the behavior of hybrid systems; typical examples are Hybrid Automata [2], Extended Duration Calculus [6], and Hybrid CSP [12]. Most of these formalisms are designed to support formal verification. But there is a fundamental problem with the formal verification of hybrid systems: the majority of such systems are not analytically tractable, only for some special types of (in)equation systems do there exist closed solutions and are algorithms known specifying how these solutions can be found. Hence, formal verification can succeed only for a few special types of problems. On the other hand, systematic testing of a hybrid system using physical prototypes or even a real environment is very expensive. Moreover, errors found during unit or integration testing are very expensive to fix. In the case of safety-critical systems, the resources needed for (regression) testing may account for more than 2/3 of the overall development budget. Simulation is therefore an essential analysis method for hybrid systems, especially if it can help to identify errors at an early stage.

The complexity of applications involving hybrid systems continues to grow rapidly. Powerful structuring means are therefore needed to describe such systems. This is one of the reasons why recently proposed simulation languages like Omola [3], Dymola [7], Smile [13], or Modelica [8] all incorporate object-oriented structuring concepts. Another advantage of the object-oriented paradigm is the adequacy of modeling physical components as objects, which leads to model components that are more reusable. The software engineering group at the TU Berlin has proposed an integrated approach to the development of object-oriented simulations of hybrid systems [4]. The main idea behind this approach is to adapt the conventional software-development process to the simulation development. Here we distinguish three main activities: design, model specification, and implementation (Fig. 1.1). The results of these activities are a set of structure diagrams, a precise and complete description of the behavioral model (ZimOO specification), and a model in an executable simulation language (Smile model description), respectively. For the last two phases, we use the object-oriented specification language ZimOO [9] and the simulation language Smile [13]. The interplay between these last two development phases was described in [4].

In this paper, we concentrate on the first phase. We describe an object-oriented notation and an accompanying methodology for the design of hybrid systems, which are based on UML (Unified Modeling Language [15]). This notation is called UMLh(hybrid UML). UML is becoming a quasi standard in OOD of discrete systems. It integrates many popular notations of OOD, including class diagrams, use-case diagrams, collaboration diagrams, and statecharts. UMLh is still limited to class diagrams, but it is planned to extend it, adapting and integrating other UML concepts for hybrid systems.

So far, little research has been done on the object-oriented design of hybrid systems, the only relevant work, to our knowledge, being the OHMS approach (Object-oriented Methodology for Hybrid Systems) [16]. There are two main differences between OHMS and UMLh. The first is that OHMS uses hybrid automata as a target language. This is a well-known formalism for hybrid-systems specification, but it is not object-oriented. This is not surprising because the main purpose of OHMS is to verify rather than simulate hybrid systems, and a powerful tool (HyTeX) is available for the symbolic verification of linear hybrid automata. As a target language for UMLh we are here using ZimOO, an object-oriented specification language, which was used as a basis for the development of UMLh. However, UMLh could, in principle, also be used in combination with other object-oriented languages for hybrid system modeling. Thus, the full power of object-oriented simulation languages can be exploited in the third development phase. The second difference between the two approaches is related to the class diagrams. OHMS provides only one general notation for a class. It can then be substituted by a hybrid automaton to describe continuous or hybrid behavior, or by a conventional automaton (a finite state machine) when the object represents purely discrete behavior. As different specification means are needed to describe discrete or continuous behavior (a method is really something quite different from a differential equation), we are convinced that — even at the design level — different notations are needed for discrete and continuous classes. UMLh therefore provides notations for three different kinds of classes: discrete, continuous, and hybrid1.

The paper is organized as follows. In Section 1.2, we introduce the UMLh notation, explaining in particular the different kinds of classes and the relations between them. Section 1.3 introduces the UMLh methodology. A graphical editor for UMLh is described in Section 1.4. In Section, 1.5 we demonstrate the applicability of the proposed approach by designing a small section of a steam-boiler system [1]. Some concluding remarks are given in Section 1.6.

1.2 NOTATION

Object-oriented design languages and methods are becoming increasingly important. They prove very helpful in managing the high complexity of the software-development process. Although practically every OOD book contains numerous descriptive examples urging the reader to view the real world as a collection of objects, a closer look at conventional OOD notations reveals that, while they are very well suited for object-oriented software development, they are only of limited suitability for the development of technical systems with discrete behavior, and they are completely inadequate when dealing with physical systems exhibiting continuous behavior. The reason for this deficiency is quite simple: the object descriptions are based on two key concepts — attributes describing the state of the object, and methods (operations) allowing this state to to be updated at certain discrete points in time. It is obvious that neither the continuous behavior of physical components nor the “continuous communication” between such components can be properly described using these concepts.

At the beginning of our project, there was no suitable graphical notation for hybrid systems. A new notation, UMLh, was therefore developed. As mentioned above, this notation is based on the Unified Modeling Language (UML) [15], thus ensuring compatibility with well-known methods. The requirements for such a notation were obtained by abstraction from specification languages for hybrid systems. The results of this analysis are the language concepts discussed in the following subsections.