Estimation of the Suboptimal Control Accuracy in the Fastest Possible Bringing of a Physical Pendulum to an Arbitrary Position

The approximate suboptimal control synthesis is considered in the classical problem of the fastest transfer of a nonlinear inertial oscillator (satellite in a circular orbit, a person on a mobile transport device, elements of controlled manipulators, exoskeletons) to an arbitrary position, in which the angular velocity is zero. The control engine torque magnitude is limited by k. In this paper, the control accuracy is estimated by mismatch of the time it takes the phase point to reach the same terminal position, when moving along different trajectories, starting from the suboptimal dispersal curve. In that case no complex numerical construction of the optimal dispersal curve is required. For various sufficiently large k, when relay control is realized by no more than one switching, and arbitrary terminal positions, not necessarily equilibrium, the accuracy estimates of the suboptimal method, phase portraits of controlled movements, switching curves, and suboptimal dispersal curves are presented.