The core Bismuth (BIS) Blockchain Layer-1 developers Prof. Geir Hovland and Jan Kucera released the academic and research paper "Nonlinear Feedback Control and Stability Analysis of a Proof-of-Work Blockchain" in 2017.
This paper talks about a novel feedback controller and stability analysis of a blockchain implementation where 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.
Recently IBM cited this paper "Nonlinear Feedback Control and Stability Analysis of a Proof-of-Work Blockchain" in Patent No .: US 10,880,073 B2
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