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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 455))

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Abstract

In this chapter, some basic concepts, definitions, and lemmas are introduced, including graph theory, multi-agent system consensus algorithms, related optimization algorithms, reinforcement learning, and game theory.

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References

  1. Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)

    Article  MATH  Google Scholar 

  2. Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Contr. 49(9), 1520–1533 (2004)

    Article  MATH  Google Scholar 

  3. Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd edn. Springer, Heidelberg (2007)

    Google Scholar 

  4. Bertsekas, D.P.: Convex Optimization Theory. Athena Scientific (2009)

    Google Scholar 

  5. Xing, H., Lin, Z., Fu, M., Hobbs, B.F.: Distributed algorithm for dynamic economic power dispatch with energy storage in smart grids. IET Control Theor. Appl. 11, 1813–1821 (2017)

    Article  Google Scholar 

  6. Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)

    Article  MATH  Google Scholar 

  7. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)

    Google Scholar 

  8. Audet, C., Hare, W.: Derivative-Free and Blackbox Optimization, vol. 2. Springer, Heidelberg (2017)

    Google Scholar 

  9. Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press (2018)

    Google Scholar 

  10. Myerson, R.B.: Game Theory. Harvard University Press (2013)

    Google Scholar 

  11. Rosen, J.B.: Existence and uniqueness of equilibrium points for concave n-person games. Econometrica 33(3), 520–534 (1965)

    Article  MATH  Google Scholar 

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Correspondence to Jiahu Qin .

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Qin, J., Wan, Y., Li, F., Kang, Y., Fu, W. (2023). Preliminaries. In: Distributed Economic Operation in Smart Grid: Model-Based and Model-Free Perspectives. Studies in Systems, Decision and Control, vol 455. Springer, Singapore. https://doi.org/10.1007/978-981-19-8594-2_2

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  • DOI: https://doi.org/10.1007/978-981-19-8594-2_2

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-8593-5

  • Online ISBN: 978-981-19-8594-2

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