Private inputs for leader-follower game with feedback Stackelberg strategy

¹ School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
² College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
³ Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, PR China

^* Corresponding author: hszhang@sdu.edu.cn

Received: 13 June 2024
Accepted: 17 April 2025

Abstract

This paper considers the two-player leader-follower game with private inputs for feedback Stackelberg strategy. In particular, the follower shares its measurement information with the leader except its historical control inputs, while the leader shares none of the historical control inputs and the measurement information with the follower. The private inputs of the leader and the follower lead to the main obstacle, which causes the estimation gain and the control gain to be related to each other, resulting in the forward and backward Riccati equations coupled and making the calculation complicated. By introducing novel observers through the information structure for the follower and the leader, respectively, a new observer-feedback Stacklberg strategy is designed. Accordingly, the obstacle mentioned above is also avoided. Moreover, it is found that the cost functions under the presented observer-feedback Stackelberg strategy are asymptotically optimal compared with the cost functions under the optimal feedback Stackelberg strategy with the feedback form of the state. Finally, a numerical example is given to show the efficiency of this paper.