Regularized classification and simulation of bifurcation regimes in nonlinear systems ?

摘要

The paper proposes a multi-step identification approach to classify a nonlinear system into qualitatively different regimes and then estimate a low-dimensional subspace where predictions of the original state at future times can be obtained by simulation of low-order dynamics. Proper Orthogonal Decomposition is used to build a library of characteristic modes from training data and is combined with regularization techniques for both the classification and estimation problems. Group Lasso is proposed to more effectively perform the former task. Moreover, ?1and ?2regularization problems with singular values weighting of the dynamic modes are suggested to handle the estimation problem in complex scenarios where limited measurement points are available or sensors are noisy. Results obtained on the Rijke tube system, a nonlinear thermoacoustic benchmark problem, demonstrate better classification accuracy and lower prediction error compared with a method from the literature.