Automatica, Vol.40, No.9, 1613-1620, 2004
Optimal regulator for the inverted pendulum via Euler-Lagrange backward integration
We present a time invariant nonlinear controller for the inverted pendulum based on optimal control, which is defined for all pendulum angles. The paper provides a case study in the brute force method of calculating the extremal field by solving the Euler-Lagrange equations backward in time, thus exploring the stable manifold of the Hamiltonian flow. The controller is only given numerically on an interpolation grid. We use this controller for closed loop simulations corroborating considerable gain robustness. (C) 2004 Elsevier Ltd. All rights reserved.
Keywords:nonlinear optimal control;Cart-pendulum system;stable manifold;Hamilton-Jacobi equation;Euler-Lagrange equations