Swing-up and Stabilization of Inverted Pendulum by Nonlinear Optimal Control

2012 Transactions of the Society of Instrument and Control Engineers  
In this paper, the problem of swing up and stabilization of an inverted pendulum by a single feedback control law is considered. The problem is formulated as an optimal control problem including input saturation and is solved via the stable manifold approach which is recently proposed for solving the Hamilton-Jacobi equation. In this approach, the problem is turned into the enhancement problem of the domain of validity to include the pending position. After a finite number of iterations, an
more » ... mal feedback control law is obtained and its effectiveness is verified by experiments. It is shown that the stable manifold approach can be applied for systems including practical nonlinearities such as saturation by directly deriving a controller satisfying the input limitation of the experimental setup. It is also reported that this system is an example in which non-unique solutions for the Hamilton-Jacobi equation exist.
doi:10.9746/sicetr.48.423 fatcat:by7txfhxofbrpe2v5olkx3nk5e