||Model predictive control (MPC) is a very popular controller design
method in the process industry. An
important advantage of MPC is that it allows the inclusion of
constraints on the inputs and outputs. Usually
MPC uses linear discrete-time models. In this project we consider
the extension of MPC to
a class of discrete event systems.
Typical examples of discrete event systems are: flexible manufacturing
networks, traffic control systems, multiprocessor operating systems,
and logistic systems. In general models
that describe the behavior of a discrete event system are nonlinear in
conventional algebra. However, there is
a class of discrete event systems - the max-plus-linear discrete event
systems - that can be described by a
model that is ``linear'' in the max-plus algebra.
Recently, we have developed an MPC framework for max-plus-linear
discrete event systems. In general the
resulting optimization problem is nonlinear and non-convex. However, if
the control objective and the
constraints depend monotonically on the outputs of the system, the MPC
problem can be recast as problem
with a convex feasible set. If in addition the objective function is
convex, this leads to a convex optimization
problem, which can be solved very efficiently.
The aim of this proposal is to further investigate several
aspects of MPC max-plus-linear
discrete event systems: development of efficient algorithms,
further investigation of which cases lead to convex
stability issues, inclusion of
disturbances, noise and modeling errors,
implementation issues (prediction, partial
information, when to update), actual
implementation on a practical example.