Stackelberg strategy for discrete-time stochastic system and its application to weakly coupled systems

Mukaidani, Hiroaki

doi:10.1109/acc.2014.6858723

Cited by 5 publications

(6 citation statements)

References 15 publications

(20 reference statements)

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“…Remark Mukaidani [20] investigated Stackelberg strategy for discrete‐time stochastic system in an infinite‐time domain, and the necessary conditions for the existence of the strategy set was derived. While, in this paper, Theorems 1‐2 establishes the necessary and sufficient conditions for the existence of optimal strategies, i.e., the necessary and sufficient solvability conditions of Stackelberg difference game are derived.…”

Section: Resultsmentioning

confidence: 99%

“…Note that the backward variable Ψ k is included in the control strategies given by ( 7) and (20), so the controllers are inexact. In order to find an exact solution, we need to establish the relationship between the variables 𝜙 k and Ψ k .…”

Section: Remark On the Feasible Solution To Problem (1)mentioning

confidence: 99%

“…It is evident that the conditional expectations are involved in Equations ( 7), (20), and (27) due to the presence of stochastic noise, making it impossible to obtain the exact optimal leader and follower's strategy, as far as we know. Alternatively, our goal is to find a feasible suboptimal solution to the considered LQ stochastic Stackelberg difference game.…”

Section: Remark On the Feasible Solution To Problem (1)mentioning

confidence: 99%

“…For k = N − 1, repeating the above steps (C1) and (C3), the leader's control strategy u L N−1 can be derived as (20).…”

Section: Appendix C: Proof Of Lemmamentioning

confidence: 99%

“…Noting that the solvability of (C4) is equivalent to the invertible of Υ L m+1 , and the leader's controller can be obtained as (20).…”

Section: Appendix C: Proof Of Lemmamentioning

confidence: 99%

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Feasible solution to discrete‐time linear quadratic stochastic Stackelberg difference game

Qi,

Zhang,

Sun

2023

Asian Journal of Control

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This paper investigates the discrete‐time linear quadratic (LQ) stochastic Stackelberg game, which has not been thoroughly addressed in previous literature. Firstly, we derive the maximum principle for the stochastic Stackelberg difference game using the variational method, and obtain the necessary and sufficient solvability conditions. However, due to the coupling between the two players and the presence of stochastic noise, obtaining explicit optimal leader and follower's strategies becomes challenging. Therefore, we present a feasible suboptimal control strategy instead. As a result, we derive a feasible suboptimal control strategy. To achieve this, we assume a linear homogeneous relationship to decouple the group of stochastic game forward‐backward stochastic differential equations (SG‐FBSDEs), which serves as a compromise for obtaining the optimal solution. With this approach, we derive a feasible solution to the stochastic Stackelberg difference game based on the solution to symmetric Riccati equations.

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Section: Resultsmentioning

confidence: 99%

Section: Remark On the Feasible Solution To Problem (1)mentioning

confidence: 99%

Section: Remark On the Feasible Solution To Problem (1)mentioning

confidence: 99%

“…For k = N − 1, repeating the above steps (C1) and (C3), the leader's control strategy u L N−1 can be derived as (20).…”

Section: Appendix C: Proof Of Lemmamentioning

confidence: 99%

“…Noting that the solvability of (C4) is equivalent to the invertible of Υ L m+1 , and the leader's controller can be obtained as (20).…”

Section: Appendix C: Proof Of Lemmamentioning