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Article

Оптимальный синтез в задаче управления n-звенным перевернутым маятником на движущемся основании

Манита Л. А., Ронжина М.

The paper is concerned with the problem of stabilization of an $n$-link inverted pendulum
on a movable base (cart). A cart is allowed to move along the horizontal axis.
A force applied to the cart is considered as a control. The problem
is to minimize the mean square deviation of the pendulum from the vertical line. For the linearized model it is shown that,
for small  deviations from the upper unstable equilibrium position, the optimal regime contains
trajectories with more and more frequent switchings. Namely, the optimal
trajectories with infinite number of switchings are shown to attain, in a finite time,
the singular surface and then continue  these  motion with singular control over the
singular surface approaching the origin in an infinite
time.  It is shown that the costructed  solutions are globally optimal.