**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.

Online version of the paper

Corresponding technical report: pdf file (269 KB)

@article{Farvan:15-034,

author={S.S. Farahani and T. van den Boom and H. van der Weide and B. {D}e Schutter},

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},

doi={10.1016/j.ejcon.2015.10.005}

}

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