Reference
S. S. Farahani, T. van den Boom, H. van
der Weide, and B. De Schutter, "An approximation method for computing the
expected value of max-affine expressions,"
European Journal of
Control, vol. 27, pp. 17-27, 2016.
Abstract
Expected values of max-affine expressions appear in optimization problems for
various stochastic systems, such as in model predictive control (MPC) for
stochastic max-plus-linear systems, in identification of stochastic
max-plus-linear systems, and in control of stochastic monotonic piecewise
affine systems. Solving these optimization problems involves the computation of
the expected value of the maximum of affine expressions, which will then appear
in the objective function or in the constraints. The computation of this
expected value can be highly complex and expensive, which also results in a
high computation time to solve the optimization problem. Therefore, the focus
of this paper is on decreasing the computational complexity of the calculation
of these expected values. To this end, we use an approximation method based on
the moments of a random variable. We illustrate in an example that this method
results in a much lower computation time and a much lower computational
complexity than the existing computational methods while still guaranteeing a
performance that is comparable to the performance of those methods.
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BibTeX
@article{Farvan:15-034,
author = {Farahani, Samira S. and van den Boom, Ton and van der Weide, Hans
and De Schutter, Bart},
title = {An Approximation Method for Computing the Expected Value of
Max-Affine Expressions},
journal = {European Journal of Control},
volume = {27},
pages = {17--27},
year = {2016}
}