Multilinear Approximation of Nonlinear State Space Models

Abstract There are numerical tools for representation, editing and simulation of continuous-time state space models, e.g. numerous block-based tools like SIMULINK. Algorithms for numerical and symbolical linearization are available but structurally fail to compute models where nonlinear effects are essential. The paper presents a numerical method to find a multilinear model as approximation which is valid in appropriate regions usually given by the engineering application. The approximate model belongs to the class of Multilinear Time Invariant systems (MTI systems) which can be represented within a tensor framework and thus, tensor decomposition methods are applicable. The proposed approximation algorithm is applied to a test case of a chemical system, which is inherently nonlinear and simulation results show the improvement of the approximation of the behaviour compared to a linear model.