Time-Optimal Movement of a Trolley with a Pendulum

摘要

We consider a system with two degrees of freedom (a pendulum on a trolley) in the case where one restricted control force is applied to the trolley. The task of a time-optimal horizontal movement to the required distance from the given equilibrium position to another identical state with the suppression of oscillations is solved. Trajectories that meet the necessary optimality conditions for the asymptotically close nonlinear system (when the mass of the pendulum is negligible in comparison with the mass of the trolley) are constructed. The results are compared with the known optimal solutions for a linearized system.