Multilinearization of polynomial models by linear state transformation

Abstract

Many problems in engineering involve the analysis and model-based control of nonlinear systems. Often a tradeoff exists between the fidelity of the model and the computational complexity of analysis and design algorithms. Multilinear models offer significant advantages in this regard since they can be represented as tensors which enables efficient representation and computation, even in high-dimensional settings. This paper deals with the multilinearization of polynomial models through linear transformation. We are able to provide a comprehensive analysis for the case of two variables. For the higher dimensional case, we propose partial solutions which exploit our results for the two-dimensional case. We perform theoretical runtime analyses of the resulting algorithms which we also illustrate through numerical results.