**Reference:**

I. Necoara,
B. De Schutter,
T.J.J. van den Boom, and
H. Hellendoorn,
"Robust control of constrained max-plus-linear systems,"
*International Journal of Robust and Nonlinear Control*, vol.
19, no. 2, pp. 218-242, Jan. 2009.

**Abstract:**

Max-plus-linear (MPL) systems are a class of nonlinear systems that
can be described by models that are "linear" in the max-plus algebra.
We provide here solutions to three types of finite-horizon min-max
control problems for uncertain MPL systems, depending on the nature of
the control input over which we optimize: open-loop input sequences,
disturbances feedback policies, and state feedback policies. We assume
that the uncertainty lies in a bounded polytope, and that the
closed-loop input and state sequence should satisfy a given set of
linear inequality constraints for all admissible disturbance
realizations. Despite the fact that the controlled system is
nonlinear, we provide sufficient conditions that allow to preserve
convexity of the optimal value function and its domain. As a
consequence, the min-max control problems can be either recast as a
linear program or solved via N parametric linear programs, where N is
the prediction horizon. In some particular cases of the uncertainty
description (e.g. interval matrices), by employing results from
dynamic programming, we show that a min-max control problem can be
recast as a deterministic optimal control problem.

Online version of the paper

Corresponding technical report: pdf file (281 KB)

@article{NecDeS:06-024,

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

title={Robust control of constrained max-plus-linear systems},

journal={International Journal of Robust and Nonlinear Control},

volume={19},

number={2},

pages={218--242},

month=jan,

year={2009},

doi={10.1002/rnc.1309}

}

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