×

Almost global stabilization of the inverted pendulum via continuous state feedback. (English) Zbl 0980.93064

The author presents a continuous feedback law which almost globally stabilizes an inverted pendulum on a cart, which means that the basin of attraction of the closed loop system is open and dense.

MSC:

93D15 Stabilization of systems by feedback
70Q05 Control of mechanical systems
70E60 Robot dynamics and control of rigid bodies
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Astrom, K. J., & Furuta, K. (1996). Swinging up a pendulum by energy control. Proceedings IFAC conference; Astrom, K. J., & Furuta, K. (1996). Swinging up a pendulum by energy control. Proceedings IFAC conference · Zbl 0941.93543
[2] Bloch, A. M., Leonard, N. E., & Marsden, J. E. (1998). Matching and stabilization by the method of controlled Lagrangians. Proceedings of the 37th IEEE CDC; Bloch, A. M., Leonard, N. E., & Marsden, J. E. (1998). Matching and stabilization by the method of controlled Lagrangians. Proceedings of the 37th IEEE CDC
[3] Fradkov, A. L., Swinging control of nonlinear oscillations, International Journal of Control, 64, 6, 1189-1202 (1996) · Zbl 0866.93049
[4] Mazenc, F.; Praly, L., Adding integrations, saturated controls and stabilizations for feedforward systems, IEEE Transactions on Automatic Control, 41, 1559-1578 (1996) · Zbl 0865.93049
[5] Shiriaev, A., Ludvigsen, H., & Egeland, O. (1998). Global stabilization of unstable equilibrium point of pendulum. Proceedings of the 37th CDC; Shiriaev, A., Ludvigsen, H., & Egeland, O. (1998). Global stabilization of unstable equilibrium point of pendulum. Proceedings of the 37th CDC · Zbl 1037.70015
[6] Shiriaev, A., Ludvigsen, H., Egeland, O., & Pogromsky, A. (1999). On global properties of passivity-based control of the inverted pendulum. Proceedings of the 38th CDC; Shiriaev, A., Ludvigsen, H., Egeland, O., & Pogromsky, A. (1999). On global properties of passivity-based control of the inverted pendulum. Proceedings of the 38th CDC · Zbl 0952.93512
[7] Sontag, E. D. (1998). Mathematical control theory; Sontag, E. D. (1998). Mathematical control theory
[8] Sontag, E. D. (1999). Stability and stabilization: discontinuities and the effect of disturbances. Nonlinear analysisdifferential equationsand control; Sontag, E. D. (1999). Stability and stabilization: discontinuities and the effect of disturbances. Nonlinear analysisdifferential equationsand control · Zbl 0937.93034
[9] Teel, A. R., A nonlinear small gain theorem for the analysis of control systems with saturation, IEEE Transactions on Automatic Control, 41, 1256-1270 (1996) · Zbl 0863.93073
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.