Closed-Loop Stackelberg Strategy for Linear-Quadratic Leader-Follower Game
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866907833573834752 |
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| author | Li, Hongdan Xu, Juanjuan Zhang, Hunashui |
| author_facet | Li, Hongdan Xu, Juanjuan Zhang, Hunashui |
| contents | This paper is concerned with the closed-loop Stackelberg strategy for linear-quadratic leader-follower game. Completely different from the open-loop and feedback Stackelberg strategy, the solvability of the closed-loop solution even the linear case remains challenging. The main contribution of the paper is to derive the explicitly linear closed-loop Stackelberg strategy with one-step memory in terms of Riccati equations. The key technique is to apply the constrained maximum principle to the leader-follower game and explicitly solve the corresponding forward and backward difference equations. Numerical examples verify the effectiveness of the results, which achieves better performance than feedback strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08977 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Closed-Loop Stackelberg Strategy for Linear-Quadratic Leader-Follower Game Li, Hongdan Xu, Juanjuan Zhang, Hunashui Optimization and Control This paper is concerned with the closed-loop Stackelberg strategy for linear-quadratic leader-follower game. Completely different from the open-loop and feedback Stackelberg strategy, the solvability of the closed-loop solution even the linear case remains challenging. The main contribution of the paper is to derive the explicitly linear closed-loop Stackelberg strategy with one-step memory in terms of Riccati equations. The key technique is to apply the constrained maximum principle to the leader-follower game and explicitly solve the corresponding forward and backward difference equations. Numerical examples verify the effectiveness of the results, which achieves better performance than feedback strategy. |
| title | Closed-Loop Stackelberg Strategy for Linear-Quadratic Leader-Follower Game |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2212.08977 |