Stabilisation of a class of 2-DOF underactuated mechanical systems via direct Lyapunov approach

References

• Acosta, J., Ortega, R., Astolfi, A., & Mahindrakar, A. (2005). Interconnection and damping assignment passivity-based control of mechanical systems with underactuation degree one. IEEE Transactions on Automatic Control, 50, 1936–1955.
   Web of Science ®Google Scholar
• Acosta, J. A. (2010). Furuta’s pendulum: A conservative nonlinear model for theory and practise. Mathematical Problems in Engineering, 2010, 29 p.
   Web of Science ®Google Scholar
• Auckly, D., Kapitanski, L., & White, W. (2000). Control of nonlinear underactuated systems. Communications on Pure and Applied Mathematics, 53, 354–369.
   Web of Science ®Google Scholar
• Bloch, A. M., Chang, D. E., Leonard, N. E., & Marsden, J. E. (2001). Controlled Lagrangians and the stabilization of mechanical systems II: Potential shaping. IEEE Transactions on Automatic Control, 46, 1556–1571.
   Web of Science ®Google Scholar
• Bloch, A. M., Leonard, N. E., & Marsden, J. E. (2000). Controlled Lagrangians and the stabilization of mechanical systems I: The first matching theorem. IEEE Transactions on Automatic Control, 45, 2253–2270.
   Web of Science ®Google Scholar
• Bullo, F., Leonard, N. E., & Lewis, A. D. (2000). Controllability and motion algorithms for underactuated Lagrangian systems on lie groups. IEEE Transactions on Automatic Control, 45, 1437–1454.
   Web of Science ®Google Scholar
• Estern, F. G., Ortega, R., Rubio, F. R., & Aracil, J. (2001). Stabilization of a class of underactuated mechanical systems via total energy shaping. Proceedings of the IEEE conference on decision and control (pp. 1137–1143), Orlando, FL, USA.
   Google Scholar
• Fantoni, I., & Lozano, R. (2002). Nonlinear control for underactuated mechanical systems (Communications and control engineering series). London: Springer-Verlag.
   Google Scholar
• Furuta, K., Yamakita, M., & Kobayashi, S. (1991). Swing-up control of inverted pendulum. Proceedings of the international conference on industrial electronics, control and instrumentation (pp. 2193–2198), Kobe, Japan.
   Google Scholar
• Ibanez, C. A. (2009). The Lyapunov direct method for the stabilisation of the ball on the actuated beam. International Journal of Control, 82, 2169–2178.
   Web of Science ®Google Scholar
• Ibanez, C. A., Castanon, M. S. S., & Gutierres-Frias, O. O. (2010). The direct Lyapunov method for the stabilisation of the Furuta pendulum. International Journal of Control, 83, 2285–2293.
   Web of Science ®Google Scholar
• Khalil, H. (2002). Nonlinear systems. Upper Saddle River, NJ: Prentice-Hall.
   Google Scholar
• Olfati-Saber, R. (2001a). Nonlinear control and reduction of underactuated systems with symmetry I: Actuated shape variables case. Proceedings of the IEEE conference on decision and control (pp. 4158–4163), Orlando, FL, USA.
   Google Scholar
• Olfati-Saber, R. (2001b). Nonlinear control of underactuated systems with application to robotics and aerospace vehicles. (PhD dissertation). Massachusetts Institute of Technology, Department of Electrical and Computer Science, Cambridge, MA, USA.
   Google Scholar
• Ortega, R., Spong, M., Gomez, F., & Blankenstein, G. (2002). Stabilization of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control, 47, 1218–1233.
   Web of Science ®Google Scholar
• Ortega, R., van der Schaft, A., Maschke, B., & Escobar, G. (2002). Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica, 38, 1137–1143.
   Web of Science ®Google Scholar
• Pettersen, K. Y. (1996). Exponential stabilization of an underactuated surface vessel. Proceedings of the IEEE conference on decision and control (pp. 962–972), Kobe, Japan.
   Google Scholar
• Reyhanoglu, M., van der Schaft, A. J., McClamroch, N. H., & Kolmanovsky, I. (1999). Dynamics and control of a class of underactuated mechanical systems. IEEE Transactions on Automatic Control, 44, 1663–1671.
   Web of Science ®Google Scholar
• Spong, M. W. (1996). Energy based control of a class of underactuated mechanical systems. Proceedings of the IFAC world congress, San Francisco, CA, USA.
   Google Scholar
• Turker, T., Gorgun, H., & Cansever, G. (2010). Stabilization of a class of 2-DOF underactuated mechanical systems via Lyapunov's direct approach. Proceedings of the 8th IFAC symposium on nonlinear control systems (pp. 1128–1133), Bologna, Italy.
   Google Scholar
• Turker, T., Gorgun, H., & Cansever, G. (2012). Lyapunov’s direct method for stabilization of Furuta’s pendulum. Turkish Journal of Electrical Engineering and Computer Sciences, 20, 99–110.
   Web of Science ®Google Scholar
• White, W. N., Foss, M., & Xin, G. (2006). A direct Lyapunov approach for a class of underactuated mechanical systems. Proceedings of the American control conference (pp. 14–16), Minneapolis, MN, USA.
   Google Scholar
• White, W. N., Foss, M., & Xin, G. (2007). A direct Lyapunov approach for stabilization of underactuated mechanical systems. Proceedings of the American control conference (pp. 4817–4822), New York City, NY, USA.
   Google Scholar
• White, W. N., Foss, M., Xin, G., & Garcia, D. (2008). Improvements in direct Lyapunov stabilization of underactuated mechanical systems. Proceedings of the American Control Conference (pp. 2927–2932), Seattle, WA, USA.
   Google Scholar