Our objective is to model and simulate Cyber-Physical Systems
(CPS) such as robots, vehicles, and power plants. The structure
of CPS models may change during simulation due to the desired operation,
due to failure situations or due to changes in physical conditions.
Corresponding models are called multi-mode. We are interested in multidomain,
component-oriented modeling as performed, for example, with
the modeling language Modelica that leads naturally to Differential Algebraic
Equations (DAEs). This paper is thus about multi-mode DAE systems.
In particular, new methods are discussed to overcome one key problem
that was only solved for specific subclasses of systems before: How
to switch from one mode to another one when the number of equations
may change and variables may exhibit impulsive behavior? An evaluation
is performed both with the experimental modeling and simulation
system Modia, a domain specific language extension of the programming
language Julia, and with SunDAE, a novel structural analysis library for
multi-mode DAE systems.
Keywords: Multi-Mode systems · Cyber-Physical Systems · CPS
Modia · Modelica · Differential algebraic equations · DAE
Differential index · Structural analysis · Operational semantics .
Constructive semantics · Nonstandard analysis