Differential Graphical Games

Kamalapurkar, Rushikesh; Walters, Patrick; Rosenfeld, Joel A.; Dixon, Warren E.

doi:10.1007/978-3-319-78384-0_5

Cited by 2 publications

(1 citation statement)

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“…The following definitions distinguish the Nash equilibrium and the Pareto optimum: Definition 3: As specified in [34], for multi-player games, for ∀i ∈ {1, • • • , N}, the Nash equilibrium…”

Section: B Differential Gamesmentioning

confidence: 99%

Differential Graphical Games for Constrained Autonomous Vehicles Based on Viability Theory

Peng

Stancu

Dang

et al. 2022

IEEE Trans. Cybern.

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This paper proposes an optimal distributed control protocol for multi-vehicle systems with an unknown switching communication graph. The optimal distributed control problem is formulated to differential graphical games, and the Pareto optimum to multi-player games is sought based on the viability theory and reinforcement learning techniques. The viability theory characterizes the controllability of a wide range of constrained nonlinear systems; and the viability kernel and the capture basin are the pillars of the viability theory. The capture basin is the set of all initial states, in which there exist control strategies that enable the states to reach the target in finite time, while remaining inside a set before reaching the target. In this regard, the feasible learning region is characterized for the reinforcement learner. In addition, the approximation of the capture basin provides the learner with prior knowledge. Unlike the existing works that employ the viability theory to solve control problems with only one agent and differential games with only two players, the viability theory, in this paper, is utilized to solve multiagent control problems and multi-player differential games. The distributed control law is composed of two parts: the approximation of the capture basin and reinforcement learning, which are computed off-line and on-line respectively. The convergence properties of the parameters' estimation errors in reinforcement learning are proved, and the convergence of the control policy to the Pareto optimum of the differential graphical game is discussed. The guaranteed approximation results of the capture basin are provided, and the simulation results of the differential graphical game are provided for multi-vehicle systems with the proposed distributed control policy.

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Section: B Differential Gamesmentioning

confidence: 99%