Hybrid Finite-Horizon Feedback Control for Cart-Pendulum Systems with Uncertainties

A methodology for the design of finite-horizon feedback control strategies is presented, with application to the cart-pendulum system. The control objective is to drive the system from an arbitrary initial state to the desired final state while minimizing the square of the control force. The optimal feedforward control for the linearized model is first derived. It is then converted into a feedback form to improve robustness to uncertainties. To simplify computations during the motion, a linearized feedback controller is introduced. To prevent the increase of the control force near the end of the control interval, an infinite-horizon feedback controller is applied. The effectiveness of the proposed control strategy is demonstrated through numerical experiments in the presence of dynamic and parametric uncertainties. Quasi-optimal trajectories and bounded control effort are achieved, offering a robust and practical solution for finite-horizon control problems.