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August 8, 2026GamesOpen Access

An Extreme Learning Machine-Based Method for Solving Linear–Quadratic Nonzero-Sum Differential Games

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Authors

CDChangdong DuanYYYuefei Yuan

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Overview

Randomized trial employs an extreme learning machine to solve nonzero-sum differential games, suggesting improved numerical stability and accuracy.

Key Points

  • This research aims to develop a reliable numerical solver for linear-quadratic differential games using extreme learning machines.
  • Recast LQ nonzero-sum game as a linear two-point boundary value problem via the Pontryagin maximum principle.
  • Utilize a single-layer feedforward neural network with fixed hidden-layer parameters sampled once.
  • Apply a stability theorem to convert continuous equation and boundary residuals into error bounds.
  • Achieved high accuracy against analytical references, confirming effectiveness in both low- and high-dimensional scenarios.
  • Tanh activation function performed best in one-dimensional problems, while Gaussian RBF excelled in higher dimensions.

Cite This Study

Duan et al. (2026) studied this question.

synapsesocial.com/papers/6a76daf2f12abadc79815b83https://doi.org/10.3390/g17040042
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