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.
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BibTeX
@article{NecDeS:06-024,
author = {Necoara, Ion and De Schutter, Bart and van den Boom, Ton J. J.
and Hellendoorn, Hans},
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}
}