Inverse LQR Construction With Retarded State Predictive Control for Systems With Time‐Delay in Input and State

In this paper, a method to design an inverse LQR with a retarded state predictor for systems with time‐delay in state and input is proposed. A feedback law is constructed by using the predictor which has a same state time‐delay as the one in the systems. It is shown that the resulting closed‐loop system is asymptotically stable and the proposed feedback law is an optimal control that minimizes a quadratic cost functional. Furthermore, we show that the constructed regulator has good robustness as same as an ordinary finite‐dimensional LQR. Finally, numerical examples are given to evaluate the effectivity of the proposed method.