Reference
S. Kanev, B. De Schutter, and M. Verhaegen, "An ellipsoid algorithm for
probabilistic robust controller design,"
Systems & Control
Letters, vol. 49, no. 5, pp. 365-375, Aug. 2003.
Abstract
In this paper a new iterative approach to probabilistic robust controller
design is presented, which is applicable to any robust controller/filter design
problem that can be represented as an LMI feasibility problem. Recently, a
probabilistic Subgradient Iteration algorithm was proposed for solving LMIs. It
transforms the initial feasibility problem to an equivalent convex optimization
problem, which is subsequently solved by means of an iterative algorithm. While
this algorithm always converges to a feasible solution in a finite number of
iterations, it requires that the radius of a non-empty ball contained into the
solution set is known
a-priori. This rather restrictive
assumption is released in this paper, while retaining the convergence property.
Given an initial ellipsoid that contains the solution set, the approach
proposed here iteratively generates a sequence of ellipsoids with decreasing
volumes, all containing the solution set. At each iteration a random
uncertainty sample is generated with a specified probability density, which
parametrizes an LMI. For this LMI the next minimum-volume ellipsoid that
contains the solution set is computed. An upper bound on the maximum number of
possible correction steps, that can be performed by the algorithm before
finding a feasible solution, is derived. A method for finding an initial
ellipsoid containing the solution set, which is necessary for initialization of
the optimization, is also given. The proposed approach is illustrated on a
real-life diesel actuator benchmark model with real parametric uncertainty, for
which a
H2 robust state-feedback controller
is designed.
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BibTeX
@article{KanDeS:02-017,
author = {Kanev, Stoyan and De Schutter, Bart and Verhaegen, Michel},
title = {An Ellipsoid Algorithm for Probabilistic Robust Controller
Design},
journal = {Systems \& Control Letters},
volume = {49},
number = {5},
pages = {365--375},
month = aug,
year = {2003}
}