Abstract
This paper designs an optimal open-loop leader-follower control strategy of input-delay stochastic systems. The leader-follower control problem is described as an optimal problem based on Stackelberg strategies. A control strategy of the leader is given to minimize the function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> norm, while a control strategy of the follower in worst case maximizing the function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> norm is applied to the systems. Then the optimal leader-follower control strategy is obtained by establishing the information relationship of the forward and the backward variables with augmentation of the variables and solving several Riccati equations. At last, an example illustrates the effectiveness of the proposed strategy.
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