“Nonlinear Feedback Control and Stability Analysis of a Proof-of-Work Blockchain”

Authors: Geir Hovland and Jan Kucera,
Affiliation: University of Agder and Bismuth Foundation
Reference: 2017, Vol 38, No 4, pp. 157-168.

Keywords: Nonlinear, control system, blockchain, feedback, stability, disturbance rejection

Abstract: In this paper a novel feedback controller and stability analysis of a blockchain implementation is developed by using a control engineering perspective. The controller output equals the difficulty adjustment in the mining process while the feedback variable is the average block time over a certain time period. The computational power (hash rate) of the miners is considered a disturbance in the model. The developed controller is tested against a simulation model with constant disturbance, step and ramp responses as well as with a high-frequency sinusoidal disturbance. Stability and a fast response is demonstrated in all these cases with a controller which adjusts it's output at every new block. Finally the performance of the controller is implemented and demonstrated on a testnet with a constant hash rate as well as on the mainnet of a public open source blockchain project.

PDF PDF (2733 Kb)        DOI: 10.4173/mic.2017.4.1

DOI forward links to this article:
[1] Jan Kucera and Geir Hovland (2018), doi:10.4173/mic.2018.3.1
[2] Pedro Pinheiro, Ricardo Santos and Ricardo Barbosa (2019), doi:10.1007/978-3-030-01746-0_39
[3] Sotirios Liaskos, Bo Wang and Nahid Alimohammadi (2019), doi:10.1109/SEAMS.2019.00025
[4] Alberto Leva, Silvia Strada and Mara Tanelli (2019), doi:10.23919/ECC.2019.8795749
[5] George Bissias, David Thibodeau and Brian N. Levine (2019), doi:10.1007/978-3-030-31500-9_24
[6] Wei Zhou (2021), doi:10.3233/JIFS-189633
[1] Booth, N. (2017). Booth, N, Kyuupichan’s Difficulty Algorithm (D578) Explained. https://tinyurl.com/y8zxvn7g, visited on Dec. 1. .
[2] Jakobsson, M. and Juels, A. (1999). Jakobsson, M, and Juels, A. Proofs of Work and Bread Pudding Protocols. In: Preneel B. (eds) Secure Information Networks. IFIP — The International Federation for Information Processing. 23:258–--272. doi:10.1007/978-0-387-35568-9_18
[3] Kucera, J. (2017). Kucera, J, Bismuth source code, release https://github.com/hclivess/Bismuth/releases, commit hash e18a9a8e99c9985f2da637d4e7cb04367a78154a. .
[4] Penard, W. and van Werkhoven, T. (2007). Penard, W, and van Werkhoven, T. On the secure hash algorithm family. https://www.staff.science.uu.nl/tel00101/liter/Books/CrypCont.pdf, visited on Nov. 19, 2017. .
[5] Rogaway, P. (2004). Rogaway, P, Nonce-Based Symmetric Encryption. Lecture Notes in Computer Science: Roy B., Meier W. (eds) Fast Software Encryption. 3017:348--358. doi:10.1007/978-3-540-25937-4_22
[6] Sechet, A. (2017). Sechet, A, Deadalnix's Difficulty Algorithm (D571) Explained. https://tinyurl.com/ycj7j2sg, visited on Dec. 2. .
[7] Smith, S.W. (1999). Smith, S, W. The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Publishing, San Diego, California, 2nd edition, 1999. .

  title={{Nonlinear Feedback Control and Stability Analysis of a Proof-of-Work Blockchain}},
  author={Hovland, Geir and Kucera, Jan},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}