Optimal conditions with chattering in the inverted two-link pendulum control problemстатья
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Дата последнего поиска статьи во внешних источниках: 5 августа 2018 г.
Аннотация:The plane motion of a two-link inverted mathematical pendulum, attached by a hinge to a moving trolley, is studied. The pendulum is controlled by a bounded force applied to the trolley. The problem of the minimization of the mean square deviation of the pendulum from an unstable equilibrium position is considered. Pontryagin's maximum principle is used. An optimal feedback control, containing singular second order trajectories and trajectories with chattering is constructed for a linearized model. It is proved that, before emerging onto a singular manifold, the optimal trajectories experience a chattering after a finite period of time and then reach the unstable equilibrium after an infinite time by a singular mode. The global optimality of the solution constructed is proved.