Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems

Zhang, Chengke; Zhou, Haiying; Ning, Bin; Zhu, Huainian

doi:10.1007/978-3-319-40587-2

Cited by 15 publications

(11 citation statements)

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“…Then, u * 1 (s) , u * 2 (s) are said to be the Nash equilibrium strategy of the differential game (10) [20].…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Remark 4 Compared to [23], the result in Theorem 3 is supplementary and practical because [23] investigated the Nash equilibrium in finite time, while this work considers the guaranteed cost Nash equilibrium in infinite time. Regarding the transition probabilities with complete transition descriptions, in [23] the solution of differential game involves four-coupled generalized difference Riccati equations [23], [20], [35], requiring an iterative algorithm [36] to solve these equations. However, this method is no longer suitable for solving optimization problems (47) that satisfy both BMIs and matrix inequalities.…”

Section: Guaranteed Cost Nash Equilibrium Strategiesmentioning

confidence: 99%

“…Definition 1 For any x 0 ∈ R n and r 0 ∈ N , the discrete-time MJLSs in (1) and (2) with control u (s) and control pair (u 1 (s) , u 2 (s)) are said to be asymptotically mean square stable, if equation lim s→∞ x T (s) x (s) , x (0) = x 0 , r 0 = i = 0 holds [20].…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Their system state equations are typically described in either a continuous-time or a discrete-time form, corresponding to the differential and difference state equations. Considering the continuous-time and discretetime MJLSs, several works [20], [21], [22], [23], [24] have studied the stochastic differential game problems such system types. It should be noted that current schemes have a common assumption stating that the transition rates can be obtained precisely in advance.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonzero-sum Stochastic Differential Gamefor Discrete-Time Markovian jump Linearsystem with incomplete transition rates

Xu¹,

Zhang²,

Li³

et al. 2022

Preprint

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This paper investigates the guaranteed cost control problem and guaranteesthe cost Nash equilibrium for discrete-time Markovian jump Linearsystem (MJLS) with incomplete transition rates. By employing matrixinequalities and the free-connection weighting matrix approach, severalsufficient conditions are proposed to ensure the applicability of theguaranteed cost control strategy. Moreover, we provide sufficient conditionsto highlight further the correctness and lower conservativeness ofthe utilized theorems. Ensuring these conditions for the existence of aguaranteed cost Nash equilibrium affords to transform them into an optimizationproblem that simultaneously satisfies a set of BMI and matrixinequalities. Furthermore, to make the results more general, this paperdesigns guaranteed cost Nash equilibrium strategies for multiple players.Finally, two detailed numerical examples validate the paper’s theorems.

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“…Then, u * 1 (s) , u * 2 (s) are said to be the Nash equilibrium strategy of the differential game (10) [20].…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Guaranteed Cost Nash Equilibrium Strategiesmentioning

confidence: 99%

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonzero-sum Stochastic Differential Gamefor Discrete-Time Markovian jump Linearsystem with incomplete transition rates

Xu¹,

Zhang²,

Li³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, in recent years, to deal with various games such as the Pareto optimal control problem and the Nash game, there have been rapid advances in the game dynamic theory for Markov jump linear stochastic systems (MJLSSs) (see e.g. [3–8]).…”

Section: Introductionmentioning

confidence: 99%

Robust incentive Stackelberg strategy for Markov jump linear stochastic systems via static output feedback

Mukaidani

Saravanakumar

2020

IET Control Theory & Applications

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Linear quadratic nonzero‐sum stochastic differential game of a partially observed Markov jump linear systems

Zhang

et al. 2022

Asian Journal of Control

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In this study, a partially observed linear quadratic (LQ) non-cooperative stochastic differential game of Markov jump linear system (MJLS) is considered. First, a new proof of filtering theory is given, using the separation principle and filtering technology, partial observations can be transformed into complete observation. Second, nonzero-sum stochastic differential game problem for MJLS are studied using the dynamic programming principle and completion square method.Then, the sufficient and necessary conditions for the Nash equilibrium are obtained. Finally, a numerical simulation is performed.

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Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems

Cited by 15 publications

References 0 publications

Nonzero-sum Stochastic Differential Gamefor Discrete-Time Markovian jump Linearsystem with incomplete transition rates

Nonzero-sum Stochastic Differential Gamefor Discrete-Time Markovian jump Linearsystem with incomplete transition rates

Robust incentive Stackelberg strategy for Markov jump linear stochastic systems via static output feedback

Linear quadratic nonzero‐sum stochastic differential game of a partially observed Markov jump linear systems

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