Approximate dissipative Hamiltonian realization and construction of local Lyapunov functions

Systems and Control Letters

Volumn 56, Issue 2, 2007, Pages 141-149

  Wang, Yuzhen ^a   Cheng, Daizhan ^b   Ge, S S ^c  

^a SHANDONG UNIVERSITY   (China)

^b INSTITUTE OF SYSTEMS SCIENCE   (China)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Algorithm; Diagonal normal form; kth degree approximate DHR; kth degree approximate Lyapunov function

Indexed keywords

ALGORITHMS; HAMILTONIANS; INVARIANCE; LINEARIZATION; NONLINEAR SYSTEMS;

DIAGONAL NORMAL FORM; DISSIPATIVE HAMILTONIAN REALIZATION (DHR); KTH DEGREE APPROXIMATE DHR; KTH DEGREE APPROXIMATE LYAPUNOV FUNCTION;

LYAPUNOV METHODS;

EID: 33845216250     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2006.08.005     Document Type: Article

References (32)

1. V.I. Arnold, Geometrical Methods on the Theory of Ordinary Differential Equations, Springer, New York, 1983, pp. 177-188.
2. Bullo F. Averaging and vibrational control of mechanical systems. SIAM J. Control Optim. 41 2 (2002) 542-562
3. D. Cheng, Z. Xi, Y. Hong, H. Qin, Energy-based stabilization in power systems, Proceedings of the 14th IFAC World Congress, Beijing, China, vol. O, 1999, pp. 297-303.
4. D. Cheng, S. Spurgeon, J. Xiang, On the development of generalized Hamiltonian realizations, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, vol. 5, 2000, pp. 5125-5130.
5. Cheng D., Hu X., and Wang Y. Non-regular feedback linearization of nonlinear systems via a normal form algorithm. Automatica 40 (2004) 439-447
6. Courant T.J. Dirac manifold. Trans. Amer. Math. Soc. 319 (1990) 631-661
7. Dalsmo M., and van der Schaft A.J. On representations and integrability of mathematical structures in energy-conserving physical systems. SIAM J. Control Optim. 37 1 (1999) 54-91
8. Devanathan R. Linearization condition through state feedback. IEEE Trans. Automat. Control 46 8 (2001) 1257-1260
9. Escobar G., van der Schaft A.J., and Ortega R. A Hamiltonian viewpoint in the modeling of switching power converters. Automatica 35 3 (1999) 445-452
10. Fantoni I., Lozano R., and Spong M.W. Energy based control of the pendubot. IEEE Trans. Automat. Control 45 4 (2000) 725-729
11. Fossen T.I. Marine Control Systems: Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles (2002), Marine Cybernetics AS, Trondheim, Norway
12. Fujimoto K., and Sugie T. Canonical transformations and stabilization of generalized Hamiltonian systems. Systems Control Lett. 42 (2001) 217-227
13. Fujimoto K., and Sugie T. Stabilization of Hamiltonian systems with nonholonomic constraints based on time-varying generalized canonical transformations. Systems control Lett. 44 (2001) 309-319
14. Galaz M., Ortega R., Bazanella A.S., and Stankovic A.M. An energy-shaping approach to the design of excitation control of synchronous generators. Automatica 39 1 (2003) 111-119
15. Ge S.S., Lee T.H., and Harris C.J. Adaptive Neural Network Control of Robotic Manipulators (1998), World Scientific, London
16. H. Khalil, Nonlinear Systems, second ed., Prentice-Hall, New Jersey, 1996.
17. Macchelli A., and Melchiorri C. Modeling and control of the Timoshenko beam: the distributed port Hamiltonian approach. SIAM J. Control Optim. 43 2 (2004) 743-767
18. B.M. Maschke, A.J. van der Schaft, Port-controlled Hamiltonian systems: modeling origins and system theoretic properties, Proceedings of the IFAC symposium on NOLCOS, Bordeaux, France, 1992, pp. 282-288.
19. Maschke B.M., Ortega R., and van der Schaft A.J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Trans. Automat. Control 45 8 (2000) 1498-1502
20. Moreau L., and Aeyels D. A novel variational method for deriving Lagrangian and Hamiltonian models of inductor-capacitor circuits. SIAM Rev. 46 1 (2004) 59-84
21. Nijmeijer H., and van der Schaft A.J. Nonlinear Dynamical Control Systems (1990), Springer, Berlin
22. Ortega R., Loría A., Nicklasson P.J., and Sira-Ramírez H. Passivity-based Control of Euler-Lagrangian Systems. Communications and Control Engineering (1998), Springer, Berlin
23. Ortega R., van der Schaft A.J., Maschke B., and Escobar G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38 4 (2002) 585-596
24. 2 disturbance attenuation of Hamiltonian systems with parameter perturbations and application to power systems, Proceedings of the 39th IEEE Conference on Decision and Control, vol. 5, 2000, pp. 4939-4944.
25. Sira-Ramírez H. A general canonical form of feedback passivity of nonlinear systems. Internat. J. Control 71 5 (1998) 891-905
26. Slotine J.E., and Li W. Applied Nonlinear Control (1991), Prentice-Hall, Englewood Cliffs, NJ
27. Stramigioli S. Modeling and IPC Control of Interactive Mechanical Systems: A Coordinate-free Approach (2001), Springer, London
28. 2-disturbance attenuation control of multimachine power systems. IEEE Trans. Automat. Control 48 8 (2003) 1428-1433
29. Wang Y., Li C., and Cheng D. Generalized Hamiltonian realization of time-invariant nonlinear systems. Automatica 39 8 (2003) 1437-1443
30. Wang Y., Li C., and Cheng D. New approaches to generalized Hamiltonian realization of nonlinear systems. Sci. in China Ser. F 46 6 (2003) 431-444
31. 2-gain and Passivity Techniques in Nonlinear Control (1999), Springer, Berlin
32. van der Schaft A.J., and Maschke B.M. The Hamiltonian formulation of energy conserving physical systems with external ports. Archive für Elektronik und Übertragungstechnik 49 (1995) 362-371