Estimation of LPV-SS models with static dependency

Numerous physical or chemical processes exhibit parameter variations due to non-stationary or nonlinear behaviour, often depending on measurable exogenous variables or measurable endogenous process states. These parameter variations can be captured in the linear parameter-varying (LPV) modeling paradigm. For control purposes, LPV state-space (SS) models are preferable, particularly with static and affine dependence on the scheduling signal. To tackle the computational complexity and perform rapid identification of LPV-SS models, a three-step approach is presented. The three steps are: 1) the estimation of the impulse response coefficients, also known as Markov coefficients, 2) an exact LPV-SS realization scheme based on these estimated Markov coefficients, and 3) an LPV-SS nonlinear optimization based refinement step. In the first step we present two possible methods: i) correlation analysis and ii) MIMO finite impulse response estimation with ridge regularization. The second step is a basis reduced, deterministic Ho-Kalman like LPV-SS realization scheme, which uses the estimated Markov coefficients of the first step. Finally, a third step is executed as a refinement step to reach the maximum likelihood estimate, for which two methods are considered i) an iterative LPV-SS expectation-maximization method and ii) an extension of the enhanced Gauss-Newton method.