Lyapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which “rocks” the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Lyapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.
Lyapunov Optimal Feedback Control of a Nonlinear Inverted Pendulum
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Anderson, M. J., and Grantham, W. J. (December 1, 1989). "Lyapunov Optimal Feedback Control of a Nonlinear Inverted Pendulum." ASME. J. Dyn. Sys., Meas., Control. December 1989; 111(4): 554–558. https://doi.org/10.1115/1.3153091
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