Private Inputs for Leader-Follower Game with Feedback Stackelberg Strategy

TL;DR

This paper introduces a novel observer-feedback Stackelberg strategy for leader-follower games with private inputs, overcoming estimation and control coupling issues, and demonstrates asymptotic optimality through a numerical example.

Contribution

It proposes a new observer-based feedback strategy that handles private information in Stackelberg games, simplifying computation and ensuring near-optimal performance.

Findings

The new strategy avoids coupled Riccati equations.

It achieves asymptotic optimality compared to the optimal feedback strategy.

Numerical results confirm the effectiveness of the proposed method.

Abstract

In this paper, the two-player leader-follower game with private inputs for feedback Stackelberg strategy is considered. 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 fact that the estimation gain and the control gain are related with each other, resulting that the forward and backward Riccati equations are coupled and making the calculation complicated. By introducing a kind of novel observers through the information structure for the follower and the leader, respectively, a kind of new observer-feedback Stacklberg strategy is designed. Accordingly, the above-mentioned obstacle is also avoided. Moreover, it is found that the cost functions under the presented observer-feedback Stackelberg strategy are asymptotically optimal to 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.