Uroš Kalabić

Michael Chiu, Uroš Kalabić

We provide a UTXO model of blockchain transactions that is able to represent both credit and debt on the same blockchain. Ordinarily, the UTXO model is solely used to represent credit and the representation of credit and debit together is achieved using the account model because of its support for balances. However, the UTXO model provides superior privacy, safety, and scalability when compared to the account model. In this work, we introduce a UTXO model that has the flexibility of balances with the usual benefits of the UTXO model. This model extends the conventional UTXO model, which represents credits as unmatched outputs, by representing debts as unmatched inputs. We apply our model to solving the problem of transparency in reverse mortgage markets, in which some transparency is necessary for a healthy market but complete transparency leads to adverse outcomes. Here the pseudonymous properties of the UTXO model protect the privacy of loan recipients while still allowing an aggregate view of the loan market. We present a prototype of our implementation in Tendermint and discuss the design and its benefits.

Uroš Kalabić, Rohit Gupta, Stefano Di Cairano et al.

We develop a model predictive control (MPC) design for systems with discrete-time dynamics evolving on smooth manifolds. We show that the properties of conventional MPC for dynamics evolving on $\mathbb R^n$ are preserved and we develop a design procedure for achieving similar properties. We also demonstrate that for discrete-time dynamics on manifolds with Euler characteristic not equal to 1, there do not exist globally stabilizing, continuous control laws. The MPC law is able to achieve global asymptotic stability on these manifolds, because the MPC law may be discontinuous. We apply the method to spacecraft attitude control, where the spacecraft attitude evolves on the Lie group SO(3) and for which a continuous globally stabilizing control law does not exist. In this case, the MPC law is discontinuous and achieves global stability.