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.
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BibTeX
@article{Xuvan:16-012,
author = {Xu, Jia and van den Boom, Ton and De Schutter, Bart},
title = {Optimistic Optimization for Model Predictive Control of Max-Plus
Linear Systems},
journal = {Automatica},
volume = {74},
pages = {16--22},
month = dec,
year = {2016}
}