**Reference:**

T.J.J. van den Boom and
B. De Schutter,
"Model predictive control of manufacturing systems with max-plus
algebra," Chapter 12 in *Formal Methods in Manufacturing* (J.
Campos, C. Seatzu, and X. Xie, eds.), *Industrial Information
Technology*, CRC Press, ISBN 978-1466561557, pp. 343-378, Feb.
2014.

**Abstract:**

Manufacturing systems can often be modeled as max-plus-linear (MPL)
systems. MPL systems are discrete-event systems with synchronization
but no choice and they are linear in the so-called max-plus algebra,
which has addition maximization as its basic operations. In this
chapter we present an in-depth account of the model predictive control
(MPC) framework for MPL systems. MPC is an on-line model based
controller design method that is very popular in the process industry
and that can also be extended to MPL systems. A key advantage of MPC
is that it can accommodate constraints on the inputs and outputs of
the controlled system. In MPC the optimal control signal is obtained
by an optimization over all possible future control sequences. In
general, the resulting MPL-MPC optimization problem is nonlinear and
nonconvex. However, we show that if the control objective is piecewise
affine, the constraints are linear, and if the control objective and
the constraints depend monotonically on the outputs of the system,
which is a frequently occurring situation for manufacturing systems,
the MPL-MPC optimization can be recast into a linear programming
problem, which can be solved very efficiently. Subsequently we focus
on implementation and timing aspects, closed-loop behavior, and tuning
rules for MPL-MPC. We derive sufficient conditions for stability and
formulate a closed-loop expression for the unconstrained MPL-MPC
controller. In the case of perturbed operation due to modeling errors
and/or noise we need a robust MPL-MPC controller. We show that under
quite general conditions the resulting optimization problems can be
solved very efficiently. For the bounded error case we also derive an
MPL-MPC controller by optimizing over feedback policies, rather than
open-loop input sequences. In general, this results in increased
feasibility and a better performance. Finally we discuss robust MPC
for MPL systems with stochastic uncertainty.

Corresponding technical report: pdf file (380 KB)

@incollection{vanDeS:14-002,

author={T.J.J. van den Boom and B. {D}e Schutter},

title={Model predictive control of manufacturing systems with max-plus algebra},

chapter={12},

booktitle={Formal Methods in Manufacturing},

series={Industrial Information Technology},

editor={J. Campos and C. Seatzu and X. Xie},

publisher={CRC Press},

pages={343--378},

month=feb,

year={2014}

}

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