Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Matrix estimation using matrix forgetting factor and instrumental variable for nonstationary sequences with time variant matrix gain

Consider us the problem of time-varying parameter estimation. The most immediate and simple idea is to include a discounting procedure in an estimation algorithm i.e., a procedure for discarding (forgetting) old information. The most common way to do is to introduce an exponential forgetting factor (FF) into the corresponding estimation procedure (to see: Ljung and Gunnarson (1990)). In this paper, the authors going to describe a good enough estimator considering a system with nonstationary time variant properties with respect to input and output qualities. The techniques used are Instrumental Variable (IV) and Matrix Forgetting Factor (MFF). The results previously obtained by (Poznyak and Medel 1999a, 1999b) were the basis of this paper. The theoretical description illustrates the advantages with respect to others filters below cited.Eje: IV - Workshop de procesamiento distribuido y paraleloRed de Universidades con Carreras en Informática (RedUNCI

Matrix estimation using matrix forgetting factor and instrumental variable for nonstationary sequences with time variant matrix gain

Consider us the problem of time-varying parameter estimation. The most immediate and simple idea is to include a discounting procedure in an estimation algorithm i.e., a procedure for discarding (forgetting) old information. The most common way to do is to introduce an exponential forgetting factor (FF) into the corresponding estimation procedure (to see: Ljung and Gunnarson (1990)). In this paper, the authors going to describe a good enough estimator considering a system with nonstationary time variant properties with respect to input and output qualities. The techniques used are Instrumental Variable (IV) and Matrix Forgetting Factor (MFF). The results previously obtained by (Poznyak and Medel 1999a, 1999b) were the basis of this paper. The theoretical description illustrates the advantages with respect to others filters below cited.Eje: IV - Workshop de procesamiento distribuido y paraleloRed de Universidades con Carreras en Informática (RedUNCI

Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set

A wide area system for power transmission security enhancement using a process systems approach

Imperial Users onl

Applications of linear estimation theory to chemical processes

Imperial Users onl

A SARIMAX coupled modelling applied to individual load curves intraday forecasting

A dynamic coupled modelling is investigated to take temperature into account in the individual energy consumption forecasting. The objective is both to avoid the inherent complexity of exhaustive SARIMAX models and to take advantage of the usual linear relation between energy consumption and temperature for thermosensitive customers. We first recall some issues related to individual load curves forecasting. Then, we propose and study the properties of a dynamic coupled modelling taking temperature into account as an exogenous contribution and its application to the intraday prediction of energy consumption. Finally, these theoretical results are illustrated on a real individual load curve. The authors discuss the relevance of such an approach and anticipate that it could form a substantial alternative to the commonly used methods for energy consumption forecasting of individual customers.Comment: 17 pages, 18 figures, 2 table