**Reference:**

S. Kanev,
B. De Schutter, and
M. Verhaegen,
"The ellipsoid algorithm for probabilistic robust controller design,"
*Proceedings of the 41st IEEE Conference on Decision and
Control*, Las Vegas, Nevada, pp. 2248-2253, Dec. 2002.

**Abstract:**

This paper presents a new iterative approach to probabilistic robust
controller design, which is an alternative to the recently proposed
Subgradient Iteration Algorithm (SIA). In its original version the SIA
possesses the useful property of guaranteed convergence in a finite
number of iterations, but requires that the radius of a non-empty ball
contained in the solution set is known *a-priori*. This rather
restrictive assumption was later on released, but only at the expense
of an increased number of iterations. The approach in this paper does
also not require the knowledge of such a radius, and offers a
significant improvement even over the original SIA in terms of the
maximum number of possible correction steps that can be executed
before a feasible solution is reached. Given an initial ellipsoid that
contains the solution set, the approach iteratively generates a
sequence of ellipsoids with decreasing volumes, all containing the
solution set. A method for finding an initial ellipsoid containing the
solution set is also proposed. The approach is illustrated on a
real-life diesel actuator benchmark model.

Corresponding technical report: pdf file (350 KB)

@inproceedings{KanDeS:02-008,

author={S. Kanev and B. {D}e Schutter and M. Verhaegen},

title={The ellipsoid algorithm for probabilistic robust controller design},

booktitle={Proceedings of the 41st IEEE Conference on Decision and Control},

address={Las Vegas, Nevada},

pages={2248--2253},

month=dec,

year={2002}

}

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