Abstract: The two cart inverted pendulum system is a good
bench mark for testing the performance of system dynamics and
control engineering principles. Devasia introduced this system to
study the asymptotic tracking problem for nonlinear systems. In this
paper the problem of asymptotic tracking of the two-cart with an
inverted-pendulum system to a sinusoidal reference inputs via
introducing a novel method for solving finite-horizon nonlinear
optimal control problems is presented. In this method, an iterative
method applied to state dependent Riccati equation (SDRE) to obtain
a reliable algorithm. The superiority of this technique has been shown
by simulation and comparison with the nonlinear approach.