The Irregular Linear Quadratic Control Problem for Deterministic Case with Time Delay

This study deals with the irregular linear quadratic control problem governed by continuous time system with time delay.Linear quadratic(LQ)control for irregular Riccati equation with time delay remains challenging since the controller could not be solved from the equilibrium condition directly.The merit of this paper is that based on a new approach of‘two-layer optimization’,the controller entries of irregular case with time delay are deduced from two equilibrium conditions in two different layers,which is fundamentally different from the classical regular LQ control.The authors prove that the irregular LQ with time delay is essentially different from the regular case.Specifically,the predictive controller bases on the feedback gain matrix and the state is given in the last part.The presented conclusions are completely new to our best knowledge.Examples is presented to show the effectiveness of the proposed approach.