A prediction-error identification framework for linear parameter-varying systems

Identification of Linear Parameter-Varying (LPV) models is often addressed in an Input-Output (IO) setting using particular extensions of classical Linear Time-Invariant (LTI) prediction-error methods. However, due to the lack of appropriate system-theoretic results, most of these methods are applied without the understanding of their statistical properties and the behavior of the considered noise models. Using a recently developed series expansion representation of LPV systems, the classical concepts of the prediction-error framework are extended to the LPV case and the statistical properties of estimation are analyzed in the LPV context. In the introduced framework it can be shown that under minor assumptions, the classical results on consistency, convergence, bias and asymptotic variance can be extended for LPV predictionerror models and the concept of noise models can be clearly understood. Preliminary results on persistency of excitation and identifiability can also established

Model structures for identification of linear parameter-varying (LPV) models

Describing nonlinear dynamic systems by linear parameter-varying models has become an attractive tool for control of complex systems with regimedependent (linear) behavior. For the identification of LPV models from experimental data a number of methods has been presented in the literature but a full picture of the underlying identification problem is still missing. In this contribution a solid system theoretic basis for the description of model structures for LPV models is presented, together with a general approach to the LPV identification problem. Use is made of a series expansion approach to LPV modeling, employing orthogonal basis function expansions

Orthonormal basis selection for LPV system identification, the Fuzzy-Kolmogorov c-Max approach

A fuzzy clustering approach is developed to select pole locations for orthonormal basis functions (OBFs), used for identification of linear parameter varying (LPV) systems. The identification approach is based on interpolation of locally identified linear time invariant (LTI) models, using globally fixed OBFs. Selection of the optimal OBF structure, that guarantees the least worst-case local modelling error in an asymptotic sense, is accomplished through the fusion of the Kolmogorov n-width (KnW) theory and fuzzy c-means (FcM) clustering of observed sample system pole

LPV system identification with globally fixed orthonormal basis functions

A global and a local identification approach are developed for approximation of linear parameter-varying (LPV) systems. The utilized model structure is a linear combination of globally fixed (scheduling-independent) orthonormal basis functions (OBFs) with scheduling-parameter dependent weights. Whether the weighting is applied on the input or on the output side of the OBFs, the resulting models have different modeling capabilities. The local identification approach of these structures is based on the interpolation of locally identified LTI models on the scheduling domain where the local models are composed from a fixed set of OBFs. The global approach utilizes a priori chosen functional dependence of the parameter-varying weighting of a fixed set of OBFs to deliver global model estimation from measured I/O data. Selection of the OBFs that guarantee the least worst-case modeling error for the local behaviors in an asymptotic sense, is accomplished through the fuzzy Kolmogorov c-max approach. The proposed methods are analyzed in terms of applicability and consistency of the estimates

Discretization of linear fractional representations of LPV systems

Commonly, controllers for Linear Parameter- Varying (LPV) systems are designed in continuous-time using a Linear Fractional Representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from continuous-time first-principle models. Existing discretization approaches for LFRs suffer from disadvantages like alternation of dynamics, complexity, etc. To overcome the disadvantages, novel discretization methods are derived. These approaches are compared to existing techniques and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling