Nuclear norm-based recursive subspace prediction of time-varying continuous-time stochastic systems via distribution theory

摘要

A method for nuclear norm-based recursive subspace prediction of time-varying continuous-time stochastic systems via distribution theory is proposed. The random distribution theory is adopted to describe the time-derivative of stochastic processes, which is the key to obtain the input-output algebraic equation. The low-rank matrix approximation of the input-output projection matrix is established by nuclear norm minimization instead of the singular value decomposition. Moreover, the optimization problem is deduced by the alternating direction method of multipliers. According to the angle rotation between past and present subspaces spanned by the extended observability matrices, the future signal subspace is predicted by the present subspace. Further, the system matrices are predicted and the corresponding system model is obtained. The results of simulation studies show the effectiveness of the presented method. (c) 2018 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.