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.

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