Ellipsoidal Bounds for Static Response of Uncertain Trusses by Using Semidefinite Programming

A semidefinite relaxation technique is proposed for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain truss. We assume that the parameters both of member stiffnesses and external forces are unknown but bounded. By using a combination of the quadratic embedding technique of the uncertainty and the S-procedure, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. Our approach has polynomial computational complexity of the problem size, if the SDP problem presented is solved by using the primal-dual interior-point method.