Active Learning for Linear Parameter-Varying System Identification

Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.

[1]  Chris Manzie,et al.  Efficient calibration of real-time model-based controllers for diesel engines — Part I: Approach and drive cycle results , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[2]  David Cohn,et al.  Active Learning , 2010, Encyclopedia of Machine Learning.

[3]  Nando de Freitas,et al.  Active Preference Learning with Discrete Choice Data , 2007, NIPS.

[4]  Xavier Bombois,et al.  Optimal experimental design for LPV identification using a local approach , 2009 .

[5]  A proof of asymptotic normality for some VARX models , 1995 .

[6]  Lars Eriksson,et al.  Modelling diesel engines with a variable-geometry turbocharger and exhaust gas recirculation by optimization of model parameters for capturing non-linear system dynamics , 2011 .

[7]  G. C. Goodwin,et al.  Optimal input signals for nonlinear-system identification , 1971 .

[8]  Stéphane Lecoeuche,et al.  On experiment design for local approach identification of LPV systems , 2018 .

[9]  Chih-Li Sung,et al.  Statistica Sinica Preprint No : SS-2016-0138 R 2 Title Exploiting Variance Reduction Potential in Local Gaussian Process , 2017 .

[10]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[11]  David J. C. MacKay,et al.  Information-Based Objective Functions for Active Data Selection , 1992, Neural Computation.

[12]  Chris Manzie,et al.  Model Predictive Controller with Average Emissions Constraints for Diesel Airpath , 2018, Control Engineering Practice.

[13]  M. Levin.  Optimum Estimation of Impulse Response in the Presence of Noise , 1960 .

[14]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[15]  Ilias Bilionis,et al.  Multi-output local Gaussian process regression: Applications to uncertainty quantification , 2012, J. Comput. Phys..

[16]  Roland Toth,et al.  Modeling and Identification of Linear Parameter-Varying Systems , 2010 .

[17]  Karl Johan Åström,et al.  BOOK REVIEW SYSTEM IDENTIFICATION , 1994, Econometric Theory.