A robust optimal trajectory tracking control for systems with an input delay

This paper proposes a robust controller for the optimal trajectory tracking problem of linear systems with an input delay and subjected to an external disturbance. We introduce a new integral transformation to convert the original error system with time delay into a delay-free one, and observe a key but simple relationship between the original state variables and the new state variables. We design the robust controller in two parts: one is a delayed optimal trajectory tracking controller used for implementing the control task, and the other is a disturbance observer used for compensating the external disturbance. Due to the delay effect, the current state in the controller is replaced with a predictor state. For demonstration, a robust controller to control the Back-and-Forth motion of an inverted pendulum on a cart is designed, where the pitch angle of the inverted pendulum is forced to be small by choosing a large weight of the pitch angle error in the quadratic performance criterion. Simulation results show that the proposed controller not only implements the control task well but also has a strong robustness against the disturbance.