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Approximation of optimal control surfaces for 2 × 2 skew-symmetric evolutionary game dynamics

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  • Nicolosi, Gabriel
  • Friesz, Terry
  • Griffin, Christopher

Abstract

In this paper we study the problem of approximating the general solution to an optimal control problem whose dynamics arise from a 2 × 2 skew-symmetric evolutionary game with arbitrary initial condition. Our approach uses a Fourier approximation method and generalizes prior work in the use of orthogonal function approximation for optimal control. At the same time we cast the fitting problem in the context of a non-standard feedforward neural network and derive the back-propagation operator in this context. An example of the efficacy of this approach is provided and generalizations are discussed.

Suggested Citation

  • Nicolosi, Gabriel & Friesz, Terry & Griffin, Christopher, 2022. "Approximation of optimal control surfaces for 2 × 2 skew-symmetric evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007329
    DOI: 10.1016/j.chaos.2022.112535
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    References listed on IDEAS

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    1. James Fan & Christopher Griffin, 2014. "Optimal Digital Product Maintenance with a Continuous Revenue Stream," Papers 1412.8624, arXiv.org, revised Feb 2017.
    2. Terry L. Friesz, 2010. "Dynamic Optimization and Differential Games," International Series in Operations Research and Management Science, Springer, number 978-0-387-72778-3, April.
    3. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    4. Jingsong Zhang & Jessica J. Cunningham & Joel S. Brown & Robert A. Gatenby, 2017. "Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    5. Askarizadeh, Mojgan & Tork Ladani, Behrouz & Manshaei, Mohammad Hossein, 2019. "An evolutionary game model for analysis of rumor propagation and control in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 21-39.
    6. Griffin, Christopher & Semonsen, Justin & Belmonte, Andrew, 2022. "Generalized Hamiltonian dynamics and chaos in evolutionary games on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    7. Katharina Kormann & Sverker Holmgren & Hans O. Karlsson, 2010. "A Fourier-Coefficient Based Solution of an Optimal Control Problem in Quantum Chemistry," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 491-506, December.
    8. Razzaghi, Mohsen & Habibi, Mohammad, 1996. "Application of Legendre series to the control problems governed by linear parabolic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 42(1), pages 77-84.
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