Nuclear norm subspace identification of continuous time state–space models with missing outputs. (February 2020) - Varanasi, Santhosh Kumar; Jampana, Phanindra
Abstract: Subspace identification methods using Generalized Poisson Moment Functionals (GPMF) have been proposed previously to tackle the problem of derivative estimation in continuous time (CT) systems. In this paper, a convergence result underpinning the GPMF methods for continuous time identification is detailed. Based on this, a CT-MOESP method is proposed to estimate the system matrices in state–space models. Since these results hold in the asymptotic case where the number of data points tend to infinity, Nuclear Norm Minimization (NNM) is used to integrate the low rank approximation step in subspace identification with a goodness of fit criterion. This paper extends these existing discrete time methods to continuous time by formulating the NNM optimization into the framework of the Alternating Direction Method of Multipliers (ADMM) algorithm. On the numerical front, the accuracy of the proposed method is demonstrated with the help of simulations on two systems frequently cited in literature. An industrial dryer application is considered in order to demonstrate the practical applicability of proposed method. Highlights: A convergence result of an IV technique in the CT-MOESP algorithm is provided. A formulation of NNM optimization in the framework of the ADMM algorithm is given. The developed approach is extended to the case of missing output data. Numerical results on systems demonstrates that the method is likely unbiased. An industrial dryer system is considered to demonstrate the practical applicability.