Optimal Control for Discrete-Time Step Backward High-Order Fully Actuated Models

This paper concerns the optimal control problem for dynamic systems represented by the discrete-time step backward high-order fully actuated (HOFA) models. A quadratic performance index of the system states is first proposed, and then for the finite-time output tracking problem and the infinite-time output regulation problem, the corresponding optimal controllers in the state feedback form are obtained as a combination of two sub-controllers: one is designed by utilizing the inherent full-actuation feature of the HOFA model to covert the original model into a linear constant model, while the other is further designed for this converted linear constant model to minimize the quadratic performance index. Finally, two simulation examples are provided to illustrate the effectiveness and superiority of our proposed optimal controllers.