Modeling and analysis of hybrid systems
Project members: B. De Schutter, W.M.P.H. Heemels (Eindhoven University of
Technology), A. Bemporad (ETH Zürich)
Sponsored by:
SICONOS (EU project)
Hybrid systems arise from the interaction between
continuousvariable systems (i.e., systems that can be
described by a system of difference or differential equations)
and discreteevent systems (i.e., asynchronous systems
where the state transitions are initiated by events; in general
the time instants at which these events occur
are not equidistant).
In general we could say that a hybrid system
can be in one of several modes whereby in each mode
the behavior of the system can be described by a
system of difference or differential equations,
and that the system switches
from one mode to another due to the occurrence of an event
(see Figure 1).
Figure 1:
Schematic representation of a hybrid system.

We have shown that several classes of hybrid systems:
piecewiseaffine systems,
mixed logical dynamical systems,
complementarity systems
and maxminplusscaling systems
are equivalent
[3,4,22,23].
Some of the equivalences are established under
(rather mild) additional assumptions.
These results are of paramount importance for transferring
theoretical properties and tools from one class to another, with
the consequence that for the study of a particular hybrid system
that belongs to any of these classes,
one can choose the most convenient hybrid modeling framework.
Related research is described under Project
4.9.
In addition, we have also shown an equivalence between
two type of mathematical programming problems:
the linear complementarity problem (LCP) and
the extended linear complementarity problem (ELCP) [14].
More specifically, we have shown that an ELCP
with a bounded feasible set can be recast as an LCP.
This result allows us to apply existing LCP algorithms
to solve ELCPs [13].
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