From Discrete Event to Hybrid Systems
Christos G. Cassandras
Abstract
Hybrid systems have emerged as a result of combining conventional time-driven dynamics with
event-driven dynamics. This provides an opportunity for frameworks and methodologies developed
for discrete event systems to enlarge their scope, driven by applications that range from
manufacturing to command-control systems. The goal of this presentation is to explore this
transition from the point of view of discrete event system theory. At least some classes
of hybrid systems may be viewed as consisting of a lower-level component that corresponds
to time-driven physical processes, which a higher-level component with event-driven dynamics
is called upon to coordinate by switching between different process operating modes. We will
concentrate on the formulation of optimization problems that arise in this “hybrid” setting,
where the control variables affect both higher and lower level components, and will invoke
optimal control methods to solve such problems. We will also discuss a natural evolution of
Perturbation Analysis (PA) techniques for discrete event systems into similar methodologies
for a class of hybrid systems known as Stochastic Fluid Models (SFM) that find wide
applicability in the control of communication networks.
Model checking embedded system designs
Ed Brinksma
Abstract
Model checking has established itself as a successful tool supported technique for the
verification and debugging of various hardware and software systems. It is also being
applied with success to the analysis of the control software in embedded systems. In our
presentation we will explain the use of model checking for such systems based on examples,
highlighting requirements, weak and strong points of the approach. We address the problem
of obtaining good models,which is less straightforward than for ordinary software systems,
as they must incorporate the relevant interaction with physical environments. Finally, we
discuss new developments based on so-called cost-driven model checking, which can be
to find (more) optimal control schedules for certain classes of embedded systems.
Recent Advances in Discrete Analysis and Control of Hybrid Systems
Bruce H. Krogh
Abstract
A standard approach to the formal analysis of hybrid systems (that is, systems with
both continuous and discrete state variables) is to first construct purely discrete-state
models, usually by building transition systems based on finite partitions of the
continuous state space. Analysis and synthesis techniques for discrete-state systems
are then applied to the discrete model to verify properties of the hybrid system and to
synthesis supervisory controllers. This approach leads to exact solutions when the
discrete-state model is a bisimulation of the hybrid system, but it is well known
that bisimulations are guaranteed to exist for only trivial classes of hybrid
systems. Consequently, developing techniques for constructing and using conservative
discrete-state models of hybrid systems has been a principal theme in hybrid systems
literature. In this paper, we review the theory for discrete analysis and control of
hybrid systems and assess the progress thus far in creating computational tools based
on this theory. The paper concludes with a discussion of several directions for research,
with an emphasis on the prospects for developing tools that can deal with problems
arising in industrial applications.
