NDLI: Approximate <inline-formula> <tex-math notation=LaTeX>$N$ </tex-math></inline-formula>-Player Nonzero-Sum Game Solution for an Uncertain Continuous Nonlinear System

Content Provider	IEEE Xplore Digital Library
Author	Johnson, M. Kamalapurkar, R. Bhasin, S. Dixon, W.E.
Copyright Year	2012
Abstract	An approximate online equilibrium solution is developed for an N-player nonzero-sum game subject to continuous-time nonlinear unknown dynamics and an infinite horizon quadratic cost. A novel actor-critic-identifier structure is used, wherein a robust dynamic neural network is used to asymptotically identify the uncertain system with additive disturbances, and a set of critic and actor NNs are used to approximate the value functions and equilibrium policies, respectively. The weight update laws for the actor neural networks (NNs) are generated using a gradient-descent method, and the critic NNs are generated by least square regression, which are both based on the modified Bellman error that is independent of the system dynamics. A Lyapunov-based stability analysis shows that uniformly ultimately bounded tracking is achieved, and a convergence analysis demonstrates that the approximate control policies converge to a neighborhood of the optimal solutions. The actor, critic, and identifier structures are implemented in real time continuously and simultaneously. Simulations on two and three player games illustrate the performance of the developed method.
Starting Page	1645
Ending Page	1658
Page Count	14
File Size	2069818
File Format	PDF
ISSN	2162237X
Volume Number	26
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Games Artificial neural networks Equations Nonlinear dynamical systems Optimal control Nash equilibrium optimal control Actor–critic (AC) methods adaptive control adaptive dynamic programming differential games
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Networks and Communications Computer Science Applications Software

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