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Regular version of the site

Article

Singularity of optimal control in the problem of stabilizing a nonlinear inverted spherical pendulum

Journal of Physics: Conference Series. 2019. Vol. 1163. P. 1-6.
Manita L., Ronzhnina M.

We study an optimal control problem for a nonlinear spherical inverted pendulum on a movable base. As the cost functional, the mean-squared deviation of the pendulum from the upper equilibrium is considered, so optimal controls stabilize the pendulum at the unstable upper position. We show that the problem under consideration posses a singular point of the second order and there are spiral-similar solution which attains the singular point in finite time.