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.

该研究解决了具有时滞的连续时间系统控制的不规则线性二次控制问题。具有时滞的不规则Riccati方程的线性二次（LQ）控制仍然具有挑战性，因为无法从平衡条件直接求解控制器。本文的优点是，基于“两层优化”的新方法，从两个不同层的两个平衡条件推导了具有时滞的不规则情况的控制器项，这与经典的常规LQ控制有根本的不同。作者证明具有时间延迟的不规则LQ与常规情况有本质的区别。具体而言，预测控制器基于反馈增益矩阵，并且在最后部分给出状态。对于我们所知，所提出的结论是全新的。举例说明了该方法的有效性。