Nonlinear Optimal Tracking Control Applied to the Rotary Inverted Pendulum

This paper discusses the nonlinear optimal tracking control problem for a class of Euler-Lagrange mechanical systems, expressed as the state-dependent coefficient factorization (SDCF), to solve the associated state-dependent Riccati equation derived from the nonlinear optimal tracking control problem. The nonlinear optimal tracking control's effectiveness is demonstrated through simulation and real-time experimental results, specifically by applying the proposed control theory to the well-known rotary inverted pendulum, a highly nonlinear and non-minimum phase system to perform time-varying reference signal tracking.