Distributed Algorithms for Searching Generalized Nash Equilibrium of Noncooperative Games

Lu, Kaihong; Jing, Gangshan; Wang, Long

doi:10.1109/tcyb.2018.2828118

Cited by 131 publications

(88 citation statements)

References 47 publications

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“…where η m and η M are positive scalars. Moreover, here we give the initial condition of system (7) as:…”

Section: Poroblem Formulationmentioning

confidence: 99%

“…Distributed parameter networked control systems with transmission delays and data packet dropouts can be modeled as a closed loops system (7) with time-varying input delays. So the method based on delay information can be used to study system (7).…”

Section: Poroblem Formulationmentioning

confidence: 99%

“…For distributed parameter NCS (7), given a feedback control gain matrix K, if the cost function defined in (10) is guaranteed to be bounded,i.e., there exists a positive constant J 0 such that J ≤ J 0 . Then, K is called as a guaranteed cost control gain of the distribution parameter NCS (7).…”

Section: Poroblem Formulationmentioning

confidence: 99%

“…The next section will provide sufficient conditions for designing the guaranteed cost control for distribution parameter NCS (7).…”

Section: T; X R; T ð þ ðmentioning

confidence: 99%

“…Due to their many advantages, such as low cost, reduced weight and power requirements, simple installation and maintenance, and high reliability, networked control systems (NCS) are frequently encountered in practice for widespread fields of applications . However, in practical NCS, there inevitably exist time delay, quantization, data packet dropouts and other uncertainties because of the introduction of the communication network, which could cause negative impact on control systems, even lead to instability.…”

Section: Introductionmentioning

confidence: 99%

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Guaranteed cost control of distributed parameter networked control systems with time‐varying delay

Zhu

2018

Asian Journal of Control

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Distributed parameter networked control systems mean distributed parameter systems are controlled through a network, where the control loops are closed. In this paper, the problem of guaranteed cost and state feedback controller design is investigated for a class of distributed parameter networked control systems. With the network factors, such as transmission delays, data packet dropouts considered, the distributed parameter networked control system is modeled as a linear closed‐loop system with time‐varying delay and uncertain parameters. By selecting an appropriate Lyapunov‐Krasovskii function and using linear matrix inequality (LMI) approach, the controller is designed to render the system stable and it can keep the cost function less than a certain upper value. In addition, numerical simulation is included to demonstrate the theoretical results.

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“…where η m and η M are positive scalars. Moreover, here we give the initial condition of system (7) as:…”

Section: Poroblem Formulationmentioning

confidence: 99%

Section: Poroblem Formulationmentioning

confidence: 99%

Section: Poroblem Formulationmentioning

confidence: 99%

“…The next section will provide sufficient conditions for designing the guaranteed cost control for distribution parameter NCS (7).…”

Section: T; X R; T ð þ ðmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Guaranteed cost control of distributed parameter networked control systems with time‐varying delay

Zhu

2018

Asian Journal of Control

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Distributed Nash equilibrium seeking for noncooperative games in nonlinear multi‐agent systems: An event‐triggered neuro‐adaptive approach

Zhang

Wang

Zhou

2021

Asian Journal of Control

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This paper proposes a distributed Nash equilibrium seeking strategy for noncooperative games over strongly connected topologies, where the players suffer from unmodeled nonlinearities and external disturbances. By using the neural network (NN) universal approximation theorem, a neuro‐adaptive seeking controller is proposed. Besides, the event‐triggered mechanism is introduced to reduce communication costs of the players. Furthermore, by developing a Lyapunov function, it is shown that the states of the players asymptotically converge to the Nash equilibrium. Finally, a simulation is conducted to show the effectiveness of the proposed methods.

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Learning‐based containment control in the absence of leaders' information

Zhao,

Fan,

Guan

2023

Engineering Reports

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This article considers the containment control problem of continuous‐time dynamic agents without leaders' state information. The leaders have first‐ and second‐order dynamics, respectively, while first‐order dynamics always govern the followers. Each agent has inherent nonlinear dynamics and can only measure the output information of its neighbors. The output of each leader is expressed as the product of an unknown coefficient and a position‐like state, while the output of each follower is equal to its position‐like state. To stabilize the position‐like states of the followers to the convex hull spanned by leaders, the unknown coefficients are asymptotically tracked by leveraging reinforcement learning based on the inherent dynamics and the output information. Two distributed learning‐based containment protocols are proposed, respectively. It is proved that if the directed communication topology has a spanning forest and certain conditions in terms of the inherent nonlinear dynamics are satisfied, then the proposed controllers with proper control gains solve the containment control problem asymptotically under arbitrary initial states. An exciting conclusion is that the learning algorithms' convergence rate plays an important role in achieving containment control. Numerical simulations are performed to validate the effectiveness of the obtained theoretical results.

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Distributed Algorithms for Searching Generalized Nash Equilibrium of Noncooperative Games

Cited by 131 publications

References 47 publications

Guaranteed cost control of distributed parameter networked control systems with time‐varying delay

Guaranteed cost control of distributed parameter networked control systems with time‐varying delay

Distributed Nash equilibrium seeking for noncooperative games in nonlinear multi‐agent systems: An event‐triggered neuro‐adaptive approach

Learning‐based containment control in the absence of leaders' information

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