**Reference:**

T.J.J. van den Boom and
B. De Schutter,
"Modeling and control of switching max-plus-linear systems with random
and deterministic switching," *Discrete Event Dynamic Systems:
Theory and Applications*, vol. 22, no. 3, pp. 293-332, Sept. 2012.

**Abstract:**

Switching max-plus-linear (SMPL) systems are discrete-event systems
that can switch between different modes of operation. In each mode the
system is described by a max-plus-linear state equation and a
max-plus-linear output equation, with different system matrices for
each mode. The switching may depend on the inputs and the states, or
it may be a stochastic process.

In this paper two equivalent descriptions for switching
max-plus-linear systems will be discussed. We will also show that a
switching max-plus-linear system can be written as a piecewise affine
system or as a constrained max-min-plus-scaling system. The last
translation can be established under (rather mild) additional
assumptions on the boundedness of the states and the inputs.

We also develop a stabilizing model predictive controller for SMPL
systems with deterministic and/or stochastic switching. In general,
the optimization in the model predictive control approach then boils
down to a nonlinear nonconvex optimization problem, where the cost
criterion is piecewise polynomial on polyhedral sets and the
inequality constraints are linear. However, in the case of stochastic
switching that depends on the previous mode only, the resulting
optimization problem can be solved using linear programming
algorithms.

Online version of the paper

Corresponding technical report: pdf file (361 KB)

@article{vanDeS:11-042,

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

title={Modeling and control of switching max-plus-linear systems with random and deterministic switching},

journal={Discrete Event Dynamic Systems: Theory and Applications},

volume={22},

number={3},

pages={293--332},

month=sep,

year={2012},

doi={10.1007/s10626-011-0123-x}

}

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