Minimum LTI exact representation of multi-parameter-dependent systems

Abstract

The aim of this paper is to propose a method that generates the minimum number of linear time-invariant systems (LTIs) used in an affine set to determine any parameter-dependent nonlinear system. The implication is to reduce the order of LTIs containing core tensor, as it can be quite large in the case of a big number of parameters, as previously every parameter was added to the parameter-space in a new dimension. Therefore, this work introduces a joint higher order singular value decomposition (HOSVD) and canonical polyadic decomposition (CPD) to derive LTIs and a joint minimum volume simplex analysis (MVSA) CPD decomposition to obtain the convex polytopic model. The results are demonstrated in the example of three degrees of freedom aeroelastic wing section.