Optimal Shortcuts to Adiabatic Control by Lagrange Mechanics

Optimal Shortcuts to Adiabatic Control by Lagrange Mechanics

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We combined an inverse engineering technique based on Lagrange mechanics and optimal control theory to design an optimal trajectory that can transport a cartpole in a fast and stable way.For classical control, we used the relative Straight Bowl Set Of 4 displacement between the ball and the trolley as the controller to study the anharmonic effect of Routers the cartpole.Under this constraint, we used the time minimization principle in optimal control theory to find the optimal trajectory, and the solution of time minimization is the bang-bang form, which ensures that the pendulum is in a vertical upward position at the initial and the final moments and oscillates in a small angle range.