Irregular LQ Optimal Control With Multiple Control Inputs and Time Delays

ABSTRACT This paper studies the irregular linear quadratic (LQ) optimal control problem involving multiple control inputs and time delays. The distinctive feature of this problem is its integration of multiple control inputs and time delays, leading to a more intricate irregular Riccati equation. This complexity stems from transforming the problem into solving time‐delayed forward–backward differential equations (D‐FBDEs). This is the crucial issue addressed in this paper. Based on the irregular theory, by constructing coupled irregular Riccati equations, the existence conditions and analytical expressions of the irregular LQ optimal control are presented. Finally, the feasibility of the results is verified through two numerical examples.