**Reference:**

J. Xu,
T. van den Boom, and
B. De Schutter,
"Optimistic optimization for model predictive control of max-plus
linear systems," *Automatica*, vol. 74, pp. 16-22, Dec. 2016.

**Abstract:**

Model predictive control for max-plus linear discrete-event systems
usually leads to a nonsmooth nonconvex optimization problem with real
valued variables, which may be hard to solve efficiently. An
alternative approach is to transform the given problem into a mixed
integer linear programming problem. However, the computational
complexity of current mixed integer linear programming algorithms
increases in the worst case exponentially as a function of the
prediction horizon. The focus of this paper is on making optimistic
optimization suited to solve the given problem. Optimistic
optimization is a class of algorithms that can find an approximation
of the global optimum for general nonlinear optimization. A key
advantage of optimistic optimization is that one can specify the
computational budget in advance and guarantee bounds on the
suboptimality with respect to the global optimum. We prove that
optimistic optimization can be applied for the given problem by
developing a dedicated semi-metric and by proving it satisfies the
necessary requirements for optimistic optimization. Moreover, we show
that the complexity of optimistic optimization is exponential in the
control horizon instead of the prediction horizon. Hence, using
optimistic optimization is more efficient when the control horizon is
small and the prediction horizon is large.

Online version of the paper

Corresponding technical report: pdf file (225 KB)

@article{Xuvan:16-012,

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

title={Optimistic optimization for model predictive control of max-plus linear systems},

journal={Automatica},

volume={74},

pages={16--22},

month=dec,

year={2016},

doi={10.1016/j.automatica.2016.07.002}

}

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