Nuclear norm subspace identification for continuous-time stochastic systems based on distribution theory method

Abstract A novel method for nuclear norm subspace identification of continuous-time stochastic systems based on distribution theory is proposed. The time-derivative problem of the system is solved by using random distribution theory, which is the key to obtain the input–output algebraic equation in the time-domain. Due to the fact that the system encounters the stochastic noise, we design a Kalman filter to achieve the state estimation and noise reduction. Nuclear norm minimization is constructed to optimize the system order in the process of subspace identification. Further, the optimization problem is solved by the alternating direction method of multipliers. Simulation results are provided to show the effectiveness of the proposed method.