Model reduction for nonlinear systems based on the differential eigenstructure of Hankel operators

This paper offers a new input-normal output-diagonal realization and model reduction procedure for nonlinear systems based on the differential eigenstructure of Hankel operators. First, we refer to the preliminary results on input-normal realizations with original singular value functions and the differential eigenstructure of Hankel operators with axis singular value functions. Next, the relationship between the two different characterizations of singular value functions is clarified and, consequently, the new input-normal realization is characterized. Finally, we perform the model reduction based on the obtained realization. Numerical examples demonstrate the effectiveness of the proposed method.

[1]  K. Fujimoto.  Synthesis and Analysis of Nonlinear Control Systems Based on Transformations and Factorizations , 2001 .

[2]  Jacquelien M. A. Scherpen,et al.  Minimality and local state decompositions of a nonlinear state space realization using energy functions , 2000, IEEE Trans. Autom. Control..

[3]  Jacquelien M.A. Scherpen,et al.  Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[4]  J. Marsden,et al.  A subspace approach to balanced truncation for model reduction of nonlinear control systems , 2002 .

[5]  J. Scherpen,et al.  Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[6]  Andrew J. Newman.  Modeling and Reduction With Applications to Semiconductor Processing , 1999 .

[7]  L. Silverman,et al.  Singular value analysis of deformable systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[8]  J. M. A. Scherpen,et al.  Balancing for nonlinear systems , 1993 .

[9]  On the nonuniqueness of balanced nonlinear realizations , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[10]  Perinkulam S. Krishnaprasad,et al.  Computation for nonlinear balancing , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[11]  A. Antoulas,et al.  A comparative study of 7 algorithms for model reduction , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[12]  Kenji Fujimoto,et al.  Eigenstructure of nonlinear hankel operators , 2001 .

[13]  Jacquelien M. A. Scherpen,et al.  On the nonuniqueness of singular value functions and balanced nonlinear realizations , 2001, Syst. Control. Lett..

[14]  Kenji Fujimoto,et al.  Hamiltonian Realizations of Nonlinear Adjoint Operators , 2000 .

[15]  Leonard M. Silverman,et al.  Singular value analysis of deformable systems , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[16]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[17]  L. Silverman,et al.  Model reduction via balanced state space representations , 1982 .