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 (ULE). The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. The resulting bounding condition is expressed as a Linear Matrix Inequality (LMI) constraint on the ellipsoid parameters and the additional scaling variables. This formulation leads to a convex optimization problem that can be efficiently solved by means of interior point barrier methods.
Bounding Ellipsoids for Uncertain LinearEquations and Dynamical Systems: the Convex Optimization Approach / Calafiore, Giuseppe Carlo; L., EL GHAOUI. - ELETTRONICO. - (2002), pp. 1-15. (Intervento presentato al convegno 15th International Symposium on Mathematical Theory of Networks and Systems tenutosi a University of Notre Dame nel August 12-16, 2002).
Bounding Ellipsoids for Uncertain LinearEquations and Dynamical Systems: the Convex Optimization Approach
CALAFIORE, Giuseppe Carlo;
2002
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 (ULE). The proposed technique is based on the combination of a quadratic embedding of the uncertainty, and the Sprocedure. The resulting bounding condition is expressed as a Linear Matrix Inequality (LMI) constraint on the ellipsoid parameters and the additional scaling variables. This formulation leads to a convex optimization problem that can be efficiently solved by means of interior point barrier methods.Pubblicazioni consigliate
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https://hdl.handle.net/11583/1408980
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