Multivariable harmonic balance for central pattern generators

Automatica

Volumn 44, Issue 12, 2008, Pages 3061-3069

  Iwasaki, Tetsuya ^a  

^a University of Virginia   (United States)

Author keywords

Harmonic balance; Neural networks; Nonlinear systems; Oscillators; Pattern generation

Indexed keywords

ADAPTIVE SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; MILITARY OPERATIONS; NEURAL NETWORKS; NEURONS; NONLINEAR SYSTEMS; OSCILLATORS (ELECTRONIC); OSCILLATORS (MECHANICAL);

ANIMAL LOCOMOTIONS; BASIC PRINCIPLES; CENTRAL PATTERN GENERATORS; CONNECTIVITY MATRIXES; CONTROL MECHANISMS; EIGENVALUE; HARMONIC BALANCE; HARMONIC BALANCES; MULTIVARIABLE; NONLINEAR OSCILLATORS; OSCILLATORS; PATTERN GENERATION; RHYTHMIC MOVEMENTS; SYSTEMATIC METHODS;

HARMONIC ANALYSIS;

EID: 53149130667     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2008.05.024     Document Type: Article

References (28)

1. Berns D., Moiola J., and Chen G. Feedback control of limit cycle amplitudes from a frequency domain approach. Automatica 34 12 (1998) 1567-1573
2. Chen Z., and Iwasaki T. Circulant synthesis of central pattern generators with application to control of rectifier systems. IEEE Transactions on Automatic Control 53 3 (2008) 273-286
3. Chen Z.Y., Zheng M., Friesen W.O., and Iwasaki T. Multivariable harmonic balance analysis of neuronal oscillator for leech swimming. Journal of Computational Neuroscience 25 3 (2008) 583-606
4. Cohen A., Rossignol S., and Grillner S. Neural control of rhythmic movements in vertebrates (1988), Wiley-Interscience
5. Crepsi A., Badertscher A., Guignard A., and Ijspeert A. Amphibot I: An amphibious snake-like robot. Robotics and Autonomous Systems 50 (2005) 163-175
6. Efimov D., and Fradkov A. Oscillation conditions of nonlinear systems with static feedback. Automation and Remote Control 66 2 (2005) 249-264
7. Fukuoka Y., Kimura H., and Cohen A. Adaptive dynamic walking of a quadruped robot on irregular terrain based on biological concepts. International Journal of Robotics Research 22 3-4 (2003) 187-202
8. Futakata Y., and Iwasaki T. Formal analysis of resonance entrainment by central pattern generator. Journal of Mathematical Biology 57 2 (2008) 183-207
9. Glad T., and Ljung L. Control theory - multivariable and nonlinear methods (2000), Taylor & Francis
10. Golubitsky M., and Stewart I. Hopf bifurcation in the presence of symmetry. Archive for Rational Mechanics and Analysis 87 2 (1985) 17-165
11. Guckenheimer J., and Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (1983), Springer-Verlag
12. Hunt K., Sbarbaro D., Zbikowski R., and Gawthrop P. Neural networks for control systems - a survey. Automatica 28 6 (1992) 1083-1112
13. Iwasaki T., and Zheng M. Sensory feedback mechanism underlying entrainment of central pattern generator to mechanical resonance. Biological Cybernetics 94 4 (2006) 245-261
14. Izhikevich E. Dynamical systems in neuroscience: The geometry of excitability and bursting (2006), The MIT Press, Cambridge, MA
15. Jonsson U., Kao C., and Megretski A. Robustness of periodic trajectories. IEEE Transactions on Automatic Control 47 11 (2002) 1842-1856
16. Khalil H. Nonlinear systems (1996), Prentice Hall
17. Lohmiller W., and Slotine J. On contraction analysis for non-linear systems. Automatica 34 6 (1998) 683-696
18. Marsden J., and McCracken M. The Hopf bifurcation and its applications (1976), Springer-Verlag, New York
19. Matsuoka K. Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biological Cybernetics 52 (1985) 367-376
20. Mees A. Dynamics of feedback systems (1981), John Wiley & Sons
21. Orlovsky G., Deliagina T., and Grillner S. Neuronal control of locomotion: From mollusc to man (1999), Oxford University Press
22. Pham Q., and Slotine J. Stable concurrent synchronization in dynamic system networks. Neural Networks 20 (2007) 62-77
23. Pogromsky A., Glad T., and Nijmeijer H. On diffusion driven oscillations in coupled dynamical systems. International Journal of Bifurcation and Chaos 9 4 (1999) 629-644
24. Pogromsky A., and Nijmeijer H. Cooperative oscillatory behavior of mutually coupled dynamical systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48 2 (2001) 152-162
25. Smale S. A mathematical model of two cells via Turing's equation. In: Marsden J.E., and McCracken M. (Eds). The Hopf bifurcation and its applications (1976), Springer-Verlag 354-367 Section 11
26. Tesi A., Abed E., Genesio R., and Wang H. Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics. Automatica 32 9 (1996) 1255-1271
27. Yakubovich V. Frequency-domain criteria for oscillation in nonlinear systems with one stationary nonlinear component. Siberian Mathematical Journal 14 5 (1973) 768-788
28. Zheng M., Friesen W., and Iwasaki T. Systems-level modeling of neuronal circuits for leech swimming. Journal of Computational Neuroscience 22 1 (2007) 21-38