LPV State-space model identification in the Bayesian setting: a 3-step procedure

Current state-of-the-art linear parameter-varying (LPV) control design methods presume that an LPV state-space (SS) model of the system with affine dependence on the scheduling variable is available. However, many existing LPV-SS identification schemes either suffer heavily from computational issues related to the curse of dimensionality or are based on severe approximations. To overcome these issues, in this paper, the Bayesian framework is combined with a recently developed efficient SS realization scheme. We propose a computationally attractive 3-step approach for identifying LPV-SS models. In Step 1, the sub-Markov parameters representing the impulse response of the system are estimated in a Bayesian setting, using kernel based Ridge regression with hyper-parameter tuning via marginal likelihood optimization. Subsequently, in Step 2, an LPV-SS realization is obtained by using an efficient basis reduced Ho-Kalman like deterministic SS realization scheme on the identified impulse response. Finally, in Step 3, to reach the maximum likelihood estimate, the LPV-SS model is refined by applying a Bayesian expectation-maximization method. The performance of the proposed 3-step scheme is demonstrated on a Monte-Carlo simulation study.