Comparison of Tensor Decomposition Methods for Simulation of Multilinear Time-Invariant Systems with the MTI Toolbox

Abstract

Several tools are available for linear state space models. But linear models may fail for applications where nonlinear effects are essential. Multilinear time-invariant (MTI) systems extend this class of systems and can be represented in a tensor framework. Tensor decomposition techniques reduce the storage effort for MTI systems and allow an efficient computation, e.g. during simulation. The paper proposes the application of four different decomposition techniques, canonic polyadic, Tucker, Tensor Train and Hierarchical Tucker decomposition to MTI systems. The methods are compared according to the application to a complex HVAC system example. The introduced MTI Toolbox implements methods for representation, simulation or linearization of MTI systems with MATLAB.