Estimation of LPV-SS Models with Static Dependency Using Correlation Analysis

Many global identification approaches described in the literature for estimating linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling parameter suffer heavily from the curse of dimensionality, making identification of moderate sized systems computationally intensive or infeasible. In this paper, we present a novel two-step approach to estimate LPV-SS models based on a single data set with varying scheduling signal by combining 1) LPV correlation analysis, and 2) a deterministic LPV realization scheme. Step 1 includes the estimation of the sub-Markov parameters of the system using correlation analysis of the involved signals. Subsequently, for Step 2, this paper presents a novel basis reduced exact Ho-Kalman like realization scheme, which uses only sub parts of the extended Hankel matrix. Therefore, the computational complexity is significantly reduced compared to the full scheme. To demonstrate that the basis reduction does not lead to a loss in performance, a simulation study is provided.