Non-steady state Kalman filter for subspace identification and predictive control

Subspace identification methods (SIMs) have drawn tremendous research interest and have been widely recognized for its computational efficiency and strong capacity in identifying MIMO systems. Most existing SIMs are based on steady-state Kalman filter (SKF) models which imply infinite horizons to be used in forming the dynamic time lags for the model. However, in practice, finite data length is the only option that dictates even shorter time horizons for the number of time lags. As a result, the SKF parameterization for SIMs can lead to suboptimal solution with finite number of data.;In this dissertation, a novel nonsteady-state Kalman filter (NKF) parameterization based SIM (NKFID) is proposed to address two aspects: finite data horizon and closed-loop identification. A progressive parameterization framework is first built to interpret the models in each stage of SIM. The model of the first stage is shown as non-parametric high order ARX model, which has applied value in model predictive control (MPC).;In practice, MPC usually assumes a step-like disturbance model which is insufficient to describe complex dynamics. The finite impulse response (FIR) model of the disturbance is recommended in this work. Two data based parameterization methods are proposed to parameterize the FIR form disturbance model. The disturbance modeling schemes with SKF parameterization is first developed to improve MPC performance. Considering finite data length, the NKF parameterization based modeling scheme is proposed and improved, and its suitability for finite data is verified theoretically. The general conversion relation between the predictor Markov parameters (PMPs) and the system Markov parameters (SMPs) is developed under the NKF framework, based on which the disturbance model is derived and incorporated to MPC.;The NKFID is proposed as a novel SIM under the NKF framework. The algorithm uses the NKF parameterization hence optimal solution is guaranteed even with limited data horizons. A routinely used projection that removes the impact of the future input is avoided to make NKFID applicable to closed-loop identification. The performance of the proposed disturbance modeling and subspace identification methods are demonstrated by several simulation examples and the benefits are verified by the comparison with existing methods.