Languages and Tools for Hybrid Systems Design

Luca P. Carloni, Roberto Passerone, Alessandro Pinto, Alberto L. Angiovanni-Vincentelli
2006 Foundations and Trends® in Electronic Design Automation  
The explosive growth of embedded electronics is bringing information and control systems of increasing complexity to every aspects of our lives. The most challenging designs are safety-critical systems, such as transportation systems (e.g., airplanes, cars, and trains), industrial plants and health care monitoring. The difficulties reside in accommodating constraints both on functionality and implementation. The correct behavior must be guaranteed under diverse states of the environment and
more » ... ntial failures; implementation has to meet cost, size, and power consumption requirements. The design is therefore subject to extensive mathematical analysis and simulation. However, traditional models of information systems do not interface well to the continuous evolving nature of the environment in which these devices operate. Thus, in practice, different mathematical representations have to be mixed to analyze the overall behavior of the system. Hybrid systems are a particular class of mixed models that focus on the combination of discrete and continuous subsystems. There is a wealth of tools and languages that have been proposed over the years to handle hybrid systems. However, each tool makes different assumptions on the environment, resulting in somewhat different notions of hybrid system. This makes it difficult to share information among tools. Thus, the community cannot maximally leverage the substantial amount of work that has been directed to this important topic. In this paper, we review and compare hybrid system tools by highlighting their differences in terms of their underlying semantics, expressive power and mathematical mechanisms. We conclude our review with a comparative summary, which suggests the need for a unifying approach to hybrid systems design. As a step in this direction, we make the case for a semantic-aware interchange format, which would enable the use of joint techniques, make a formal comparison between different approaches possible, and facilitate exporting and importing design representations. 1 George Pappas research group at the Univ. of Pennsylvania is maintaining a WikiWiki-Web site at graspdoc/hst/ whose objective is to serve as a community depository for software tools that have been developed for modeling, verifying, and designing hybrid and embedded control systems. It provides an "evolving" point of reference for the research community as well as potential users of all available technology and it maintains updated links to online resources for most of the tools listed on Table 1.1. 9 2.1. Formal definition of hybrid systems 11 considering classes of discrete dynamical systems underlying each state. The triple (Q, U D , E) can be viewed as an automaton having state set Q, inputs U D and transitions defined by E. This automaton characterizes the structure of the discrete transitions. Transitions may occur because of a discrete input event from U D , or because the invariant in Inv is not satisfied. The mapping S provides the association between the continuous time definition of the dynamical system in terms of differential equations and the discrete behavior in terms of states. The mapping R provides the initial conditions for the dynamical system upon entering a state. The transition and dynamical structure of a hybrid system determines a set of executions. These are essentially functions over time for the evolution of the continuous state, as the system transitions through its discrete structure. To highlight the discrete structure, we introduce the concept of a hybrid time basis for the temporal evolution of the system, following [129]. Definition 2.2. (Hybrid Time Basis) A hybrid time basis τ is a finite or an infinite sequence of intervals where t j ≤ t j and t j = t j+1 .
doi:10.1561/1000000001 fatcat:e27dfodqcranhememam757wdj4