Optimal control for linear discrete-time systems with persistent disturbances

This paper is concerned with the optimal control problem for a class of linear discrete-time systems affected by external persistent disturbances with known dynamic characteristics but unknown initial conditions. The existence and uniqueness of an optimal control law are proven. A disturbance observer is designed to get a physically realizable controller. To demonstrate the effectiveness of the control scheme, the offshore platform performance is investigated. The simulations are based on the tuned mass damper (TMD) and the active mass damper (AMD) control devices. It is demonstrated that the control scheme is efficient in reducing the displacement response of jacket-type offshore platforms and more robust than the classic state feedback optimal control law with respect to errors produced by the external disturbances.