Ellipsoidal bounds for uncertain linear equations and dynamical systems

Authors:
Giuseppe Calafiore;Laurent El Ghaoui
Affiliations:
Dipartimento di Automatica e Informatica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino 10129, Italy;Dept. of Electrical Engineering and Computer Science, University of California at Berkeley, Berkely, CA, USA
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

In this paper, we discuss semidefinite relaxation techniques for computing minimal size ellipsoids that bound the solution set of a system of uncertain linear equations. The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the S-procedure. This formulation leads to convex optimization problems that can be essentially solved in O(n^3)-n being the size of unknown vector-by means of suitable interior point barrier methods, as well as to closed form results in some particular cases. We further show that the uncertain linear equations paradigm can be directly applied to various state-bounding problems for dynamical systems subject to set-valued noise and model uncertainty.