||Recently we have extended the model predictive
control (MPC) framework to some
classes of hybrid systems
such as traffic-signal-controlled
and first order linear hybrid systems with
General hybrid systems arise from the interaction between
continuous variable systems (i.e.,
systems that can be described by a difference or differential
equation) and discrete event
systems where the state transitions are initiated by events that occur
at discrete time instants).
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 events (see the figure below).
Typical examples of hybrid systems are flexible manufacturing
systems, transportation networks, beer brewing processes,
logistic systems, etc.
The aim of this proposal is to further investigate several
aspects of MPC for hybrid systems:
for which classes of systems can the resulting optimization
problems be solved efficiently (e.g., via convex optimization),
development of efficient algorithms,
stability issues, inclusion of
disturbances, noise and modeling errors,
implementation issues (prediction, partial
information, when to update), and actual
implementation on a practical example.