Fast convergence to Nash equilibria without steady-state oscillation

Zahedi, Zahra; Arefi, Mohammad Mehdi; Khayatian, Alireza

doi:10.1016/j.sysconle.2018.11.009

Cited by 9 publications

(24 citation statements)

References 23 publications

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“…, which explicitly demonstrates the effectiveness of the ESO (10) an the ADO (15). Finally, Figure 12 gives the time histories of the adaptive gains i,j , i, j = 1, … , 6, which are steered to converge to some positive values.…”

Section: Competition Among Energy Resources Of Generation Systemsmentioning

confidence: 92%

“…with i,j ∈ R + and i,j (0) ∈ R + . It is worth noting that if player j is a neighbor of player i or j = i, then the update of y i, j can be excluded from (15). However, we keep it for notational convenience.…”

Section: Ado Designmentioning

confidence: 99%

“…The generalized Nash equilibrium seeking problems were investigated in References 11,12. Extremum seeking‐based algorithms were developed in References 13‐15 to address noncooperative games with nonquadratic payoffs.…”

Section: Introductionmentioning

confidence: 99%

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Distributed adaptive Nash equilibrium seeking and disturbance rejection for noncooperative games of high‐order nonlinear systems with input saturation and input delay

Wang

2021

Intl J Robust & Nonlinear

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This article aims to investigate Nash equilibrium seeking problems for noncooperative games played by high-order nonlinear multiagent systems subject to input saturation, input delay, and external disturbances. Based on the gradient play technique, an adaptive Nash equilibrium seeking algorithm is designed in a distributed fashion via backstepping, where a fixed-time sliding mode observer is used to tackle the problem of "explosion of terms." In the proposed algorithm, an extended-state observer and an adaptive distributed observer are included for state/disturbance estimates and information sharing, respectively. Detailed convergence results are presented by leveraging Lyapunov stability theory. Finally, the effectiveness of the proposed approach is numerically verified through simulation results.

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Section: Competition Among Energy Resources Of Generation Systemsmentioning

confidence: 92%

Section: Ado Designmentioning

confidence: 99%

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Distributed adaptive Nash equilibrium seeking and disturbance rejection for noncooperative games of high‐order nonlinear systems with input saturation and input delay

Wang

2021

Intl J Robust & Nonlinear

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“…However, in some practical engineering systems, there exist unknown cost functions, constraints and other parameters in games, such as unknown price functions in energy markets [34], the power function without explicit aerodynamic interactions in the wind turbine [35], unknown traffic demands/constraints in the network routing [36], and unknown position information and/or environmental conditions in mobile sensor networks [2]. To deal with such situations, an adaptive and real-time method, called extremum seeking control (ESC) [46], [39], [37], [38], was introduced in distributed seeking algorithms [2], [3], [31], [33]. In this paper, we explore how to steer agents to update their strategies adaptively to GNE under the conditions of unknown cost functions and local constraints.…”

Section: Introductionmentioning

confidence: 99%

“…For N -person noncooperative static games, the classical ESC method was used to solve the NE [2], [3], [31]. To eliminate steady-state oscillations, an extremum seeking method with fast convergence was designed to seek the NE [33]. The comparison between the existing algorithms and our proposed method is shown in Table I.…”

Section: Introductionmentioning

confidence: 99%

A distributed generalized Nash equilibrium seeking algorithm based on extremum seeking control

Xing¹,

X²,

Wei³

2022

Preprint

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In this paper, a distributed non-model based seeking algorithm which combines the extremum seeking control (ESC) jointly with learning algorithms is proposed to seek a generalized Nash equilibrium (GNE) for a class of noncooperative games with coupled equality constraint. The strategy of each agent is restricted by both the coupled inter-agent constraint and local inequality constraints. Thanks to the ESC, it is unnecessary to know the specific expressions of agents' cost functions and local constraints and to know the strategies of other agents for the implementation of the proposed GNE seeking algorithm. To deal with the coupled constraints, only the Lagrange multiplier is transmitted among agents with some prior information about the coupled constraints. Moreover, a diminishing dither signal is designed in the seeking algorithm to remove undesirable steady-state oscillations. The non-local convergence of the designed seeking algorithm is analyzed via the singular perturbation theory, averaging analysis and Lyapunov stability theory. Numerical examples are given to verify the effectiveness of our proposed method.

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Distributed generalized Nash equilibrium seeking for noncooperative games with unknown cost functions

Cai

Xiao

Wei

2022

Intl J Robust & Nonlinear

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In this article, a distributed nonmodel based generalized Nash equilibrium (GNE) seeking algorithm is proposed for a class of constrained noncooperative games with unknown cost functions. In the game, the strategy of each agent is restricted by both the coupled equality constraint and local inequality constraints. By virtue of the exact penalty method, an auxiliary cost function is constructed with the cost function and the local constraints. The main feature of the proposed algorithm depends on the capability to estimate the gradient information of auxiliary cost functions with only the values of costs. This is obtained by the extremum seeking control (ESC). To deal with the coupled constraints, only the Lagrange multiplier is transmitted among agents with some prior information about the coupled constraints. Moreover, a diminishing dither signal is introduced in the seeking algorithm to remove undesirable steady-state oscillations occurred in the classical ESC. As a result, the nonlocal convergence of the designed seeking algorithm to the GNE of the game is obtained by the singular perturbation theory, averaging analysis and Lyapunov stability theory. Numerical examples are given to verify the effectiveness of our proposed method.

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Fast convergence to Nash equilibria without steady-state oscillation

Cited by 9 publications

References 23 publications

Distributed adaptive Nash equilibrium seeking and disturbance rejection for noncooperative games of high‐order nonlinear systems with input saturation and input delay

Distributed adaptive Nash equilibrium seeking and disturbance rejection for noncooperative games of high‐order nonlinear systems with input saturation and input delay

A distributed generalized Nash equilibrium seeking algorithm based on extremum seeking control

Distributed generalized Nash equilibrium seeking for noncooperative games with unknown cost functions

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