论文信息 - A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems

A Kernel Subspace Method by Stochastic Realization for Learning Nonlinear Dynamical Systems

In this paper, we present a subspace method for learning nonlinear dynamical systems based on stochastic realization, in which state vectors are chosen using kernel canonical correlation analysis, and then state-space systems are identified through regression with the state vectors. We construct the theoretical underpinning and derive a concrete algorithm for nonlinear identification. The obtained algorithm needs no iterative optimization procedure and can be implemented on the basis of fast and reliable numerical schemes. The simulation result shows that our algorithm can express dynamics with a high degree of accuracy.

Yoshinobu Kawahara | Takehisa Yairi | Kazuo Machida

[1] G. Rota. Stationary random processes associated with point processes , 1985 .

[2] J. Suykens,et al. Least Squares Support Vector Machines for Kernel CCA in Nonlinear State-Space Identification , 2004 .

[3] Tohru Katayama,et al. Subspace Methods for System Identification , 2005 .

[4] Alexander J. Smola,et al. Learning with kernels , 1998 .

[5] Malte Kuss,et al. The Geometry Of Kernel Canonical Correlation Analysis , 2003 .

[6] J. Suykens,et al. Subspace identification of Hammerstein systems using least squares support vector machines , 2005 .

[7] Michael I. Jordan,et al. Kernel independent component analysis , 2003 .

[8] Michael I. Jordan,et al. Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces , 2004, J. Mach. Learn. Res..

[9] Giorgio Picci,et al. Realization of stochastic systems with exogenous inputs and subspace identification methods , 1999, Autom..

[10] Henk B. Verbruggen,et al. A new method for identification and control of nonlinear dynamic systems , 1996 .

[11] Zoubin Ghahramani,et al. A Unifying Review of Linear Gaussian Models , 1999, Neural Computation.