Optimal Swing Up and Stabilization Control for Inverted Pendulum via Stable Manifold Method

This brief addresses the problem of swing up and stabilization for inverted pendulum. It is shown that the stable manifold method, recently proposed for approximately solving Hamilton-Jacobi equation (HJE) in nonlinear optimal control problem, is capable of designing feedback control for this problem. The experimental results include two types of controllers (one-swing and two-swing), which indicates the nonuniqueness of solution for an HJE. This brief further provides a variational analysis method for investigating and enlarging a stable manifold and shows a detail structure of the stable manifold for a 2-D pendulum from which controllers from one-swing to five-swing can be derived.