Indefinite Mean-Field Stochastic Cooperative Linear-Quadratic Dynamic Difference Game With Its Application to the Network Security Model

Zhang, Weihai; Peng, Chenchen

doi:10.1109/tcyb.2021.3070352

Cited by 21 publications

(15 citation statements)

References 38 publications

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“…Simulation results of a numerical example have shown the effectiveness of the main results. In the future, we can extend the obtained Pareto optimal strategy under H ∞ constraint to the infinite horizon case [13] or apply it to the mean-field stochastic system [23] and time-delay system [33]. We can also explore model-free Pareto optimal control under H ∞ constraint through reinforcement learning methods [34].…”

Section: Discussionmentioning

confidence: 99%

“…Then by solving the Equations ( 20) and ( 22), we get P 10 v and P 10 u . Calculate like this until k=0, we get evolutions of P k v = P v11 P v12 P v12 P v22 , P k u = P u11 P u12 P u12 P u22 , K k γ and K k p shown in Figures 1 and 2, respectively, which show the convergence of the solutions of coupled GDREs ( 20)- (23). From Figures 3 and 4, we can konw that the constraints P k v ≤ 0 and P 0 v + γ 2 S > 0 are satisfied, which means that the obtained P k v and P k u are valid.…”

Section: Proof Of Theorem 2 Since We Have Knownmentioning

confidence: 99%

“…Remark 3. It can be seen from Theorem 1 that the Pareto optimal control under the worst-case disturbance can be obtained by solving the coupled GDREs ( 20)- (23). Different from the reference [16], the results in Theorem 1 take into account both Pareto optimality and H ∞ performance, and are about finite horizon.…”

Section: Lemma 8 ([32]mentioning

confidence: 99%

“…The development of Pareto optimal control theory is inseparable from the progress of linear quadratic (LQ) dynamic game theory. The stochastic LQ optimal control problem was proposed initially by Wonham [20] and attracted great attention of many scholars [21][22][23]. Chen et al [24] found that a stochastic LQ problem with indefinite cost weighting matrices can still be well-posed.…”

Section: Introductionmentioning

confidence: 99%

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Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

et al. 2022

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This paper investigates the Pareto optimal strategy of discrete-time stochastic systems under H∞ constraint, in which the weighting matrices of the weighted sum cost function can be indefinite. Combining the H∞ control theory with the indefinite LQ control theory, the generalized difference Riccati equations (GDREs) are obtained. By means of the solution of the GDREs, the Pareto optimal strategy with H∞ constraint is derived, and the necessary and sufficient conditions for the existence of the strategy are presented. Then the Pareto optimal solution under the worst-case disturbance is solved. Finally, the efficiency of the obtained results is illustrated by a numerical example.

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Section: Discussionmentioning

confidence: 99%

Section: Proof Of Theorem 2 Since We Have Knownmentioning

confidence: 99%

Section: Lemma 8 ([32]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

et al. 2022

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“…However, to the best knowledge of authors, there is no work addressing the non-fragile finite-time controller design for LDMFS systems. Up to now, for LDMFS systems, we can only find few work such as [7] on linear quadratic optimal control problem and [38] about cooperative linear quadratic dynamic difference game.…”

Section: Introductionmentioning

confidence: 99%

Non-fragile Finite-time Stabilization for Discrete Mean-field Stochastic Systems

Zhang¹,

Deng²,

Shi³

2022

Preprint

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In this paper, the problem of non-fragile finitetime stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli distribution. A new approach called the "state transition matrix method" is introduced and some necessary and sufficient conditions are derived to solve the underlying stabilization problem. The Lyapunov theorem based on the state transition matrix also makes a contribution to the discrete finite-time control theory. One practical example is provided to validate the effectiveness of the newly proposed control strategy.

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Cooperative linear quadratic differential games for uncertain systems with conservative players

Zhang

Shi

Zhong

2023

Asian Journal of Control

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This paper investigates cooperative linear quadratic differential games for uncertain dynamic systems with conservative players, who attempt to optimize the worst‐case outcomes with limited a priori knowledge about the uncertainties. Without properly designed control strategies, the uncertainties could cause significant impacts on the performance indexes of players and spoil the cooperation among players. In this paper, compensation‐based robust control techniques are applied to handle the uncertainties, including parameter perturbations and external disturbances, by transforming the impacts of the uncertainties into a more tractable form. Subsequently, using Vickrey–Clarke–Groves principles, an auction‐based control allocation mechanism is designed to incentivize the players to cooperatively implement the compensation. With the methods proposed, the worst‐case performance indexes of players can be improved, and the cooperation among players is maintained in the uncertain system. Numerical examples demonstrate the effectiveness of the proposed methods.

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Indefinite Mean-Field Stochastic Cooperative Linear-Quadratic Dynamic Difference Game With Its Application to the Network Security Model

Cited by 21 publications

References 38 publications

Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

Non-fragile Finite-time Stabilization for Discrete Mean-field Stochastic Systems

Cooperative linear quadratic differential games for uncertain systems with conservative players

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