Balanced realization and model reduction of port-Hamiltonian systems

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 930-934

  Fujimoto, Kenji ^a   Kajiura, Hideo ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BESSEL FUNCTIONS; COMPUTER SIMULATION; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES; PORTS AND HARBORS; SYSTEM STABILITY;

(PL) PROPERTIES; BALANCED REALIZATION (BR); COMPUTATIONAL EFFORTS; DISSIPATIVITY; ELECTRO MECHANICAL SYSTEMS; MODEL REDUCTIONS; NONLINEAR MODEL REDUCTION; NUMERICAL SIMULATIONS; ORIGINAL SYSTEMS; PARTIAL DIFFERENTIAL; PHYSICAL ENERGY; PORT-HAMILTONIAN STRUCTURE; PORT-HAMILTONIAN SYSTEMS; REACH ABILITY; REDUCED-ORDER-MODEL (ROM);

HAMILTONIANS;

EID: 46449116816     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282653     Document Type: Conference Paper

References (20)

1. K. Fujimoto. What are singular values of nonlinear operators? In Proc. 43rd IEEE Conf. on Decision and Control, pages 1623-1628, 2004.
2. K. Fujimoto and J. M. A. Scherpen. Nonlinear balanced realization based on singular value analysis of Hankel operators. In Proc. 42nd IEEE Conf. on Decision and Control, pages 6072-6077, 2003.
3. K. Fujimoto and J. M. A. Scherpen. Nonlinear input-normal realizations based on the differential eigenstructure of Hankel operators. IEEE Trans. Autom. Contr., 50(1):2-18, 2005.
4. K. Fujimoto and T. Sugie. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters, 42(3):217-227, 2001.
5. K. Fujimoto and T. Sugie. Iterative learning control of Hamiltonian systems: I/O based optimal control approach. IEEE Trans. Autom. Contr., 48(10):1756-1761, 2003.
6. K. Fujimoto and D. Tsubakino. On computation of nonlinear balanced realization and model reduction. In Proc. American Control Conference, pages 460-465, 2006.
7. J. Hahn and T. F. Edgar. Reduction of nonlinear models using balancing of empirical gramians and Galerkin projections. In Proc. American Control Conference, pages 2864-2868, 2000.
8. R. Lopezlena, J. M. A. Scherpen, and K. Fujimoto. Energy-storage balanced reduction of port Hamiltonian systems. In Proc. IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, pages 79-84, 2003.
9. B. C. Moore. Principal component analysis in linear systems: controllability, observability and model reduction. IEEE Trans. Autom. Contr., AC-26:17-32, 1981.
10. A. Newman and P. S. Krishnaprasad. Computing balanced realizations for nonlinear systems. In Proc. Symp. Mathematical Theory of Networks and Systems, 2000.
11. A. J. Newman and P. S. Krishnaprasad. Computation for nonlinear balancing. In Proc. 37th IEEE Conf. on Decision and Control, pages 4103-4104, 1998.
12. G. Obinata and B. D. O. Anderson. Model Reduction for Control System Design. Springer-Verlag, London, 2001.
13. R. Ortega, A. J. van der Schaft, B. M. J. Maschke, and G. Escobar. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica, 38(4):585-596, 2002.
14. J. M. A. Scherpen. Balancing for nonlinear systems. Systems & Control Letters, 21:143-153, 1993.
15. J. M. A. Scherpen and W. S. Gray. Minimality and local state decompositions of a nonlinear state space realization using energy functions. IEEE Trans. Autom. Contr., AC-45(11):2079-2086, 2000.
16. J. M. A. Scherpen and A. J. van der Schaft. Normalized coprime factorization and balancing for unstable nonlinear systems. Int. J. Control, 60(6)1193-1222, 1994.
17. D. Tsubakino and K. Fujimoto. Weighted balanced realization and model reduction for nonlinear systems. In Proc. Symp. Mathematical Theory and Network Systems 2006, 2006.
18. 2-Gain and Passivity Techniques in Nonlinear Control. Springer-Verlag, London, 2000.
19. H. A. van der Vorst. Iterative Krylov Methods for Large Linear Systems. Cambridge University Press, Cambridge, 2003.
20. E. I. Verriest and W. S. Gray. Discrete-time nonlinear balancing. In Proc. 5th IFAC Symp. Nonlinear Control Systems, pages 515-520, 2001.