Control-oriented modelling of proof-of-work blockchains

Blockchain (BC) technology is a rather new conception of a mixed hardware and software platform to achieve distributed consensus among peers. Its diffusion is related to cryptocurrency, the most widespread of which is Bitcoin. The protocol on which BCs operate sees the interaction between users, interested in performing their transactions, and miners, who certify the trust behind the transactions by putting some form of effort that allows acknowledging their trustfulness, obtaining Bitcoins in reward for their work. In the so-called proof-of-work implementation of the BC, such effort is the computational power needed to find a specific string of bits called nonce. The resulting game-theoretic setting has subtle dynamics, and its functioning could be strongly improved using closed-loop control. This work is an attempt to define a control-oriented description of the agent-based BC dynamics and offer a redesign of the difficulty control system that regulates the amount of work needed to add a new trusted block to the BC. This control loop directly relates to the energy consumption of the overall system, which is one of the major drivers that will determine the future sustainability of the BC paradigm.