Optimal Swing Up and Stabilization Control for Inverted Pendulum via Stable Manifold Method
Takamasa Horibe, Noboru Sakamoto · IEEE Transactions on Control Systems Technology · 2017
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.