arXiv subjects

Uroš Kalabić

Publications and source records attributed to Uroš Kalabić.

5 recordsLinked to original sources

arXiv2021

Debt Representation in UTXO Blockchains

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.

cs.CR↗

arXiv2020

A constraint-separation principle in model predictive control

In this brief, we consider the constrained optimization problem underpinning model predictive control (MPC). We show that this problem can be decomposed into an unconstrained optimization problem with the same cost function as the original problem and a constrained optimization problem with a modified cost function and dynamics that have been precompensated according to the solution of the unconstrained problem. In the case of linear systems subject to a quadratic cost, the unconstrained problem has the familiar LQR solution and the constrained problem reduces to a minimum-norm projection. This implies that solving linear MPC problems is equivalent to precompensating a system using LQR and applying MPC to penalize only the control input. We propose to call this a constraint-separation principle and discuss the utility of both constraint separation and general decomposition in the design of MPC schemes and the development of numerical solvers for MPC problems.

math.OC↗

arXiv2020

Optimization-based incentivization and control scheme for autonomous traffic

We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the theory and methods of optimal transport, we propose a constrained optimization framework over dynamics governed by partial differential equations, so that we can optimally select a portion of vehicles to be incentivized and controlled. The goal of the optimization is to obtain a uniform distribution of vehicles over the spatial domain. To achieve this, we consider two types of penalties on vehicle density, one is the $L^2$ cost and the other is a multiscale-norm cost, commonly used in fluid-mixing problems. To solve this non-convex optimization problem, we introduce a novel algorithm, which iterates between solving a convex optimization problem and propagating the flow of uncontrolled vehicles according to the Lighthill-Whitham-Richards model. We perform numerical simulations, which suggest that the optimization of the $L^2$ cost is ineffective while optimization of the multiscale norm is effective. The results also suggest the use of a dedicated lane for this type of control in practice.

math.OC↗

arXiv2019

Application of Pontryagin's Minimum Principle to Grover's Quantum Search Problem

Grover's algorithm is one of the most famous algorithms which explicitly demonstrates how the quantum nature can be utilized to accelerate the searching process. In this work, Grover's quantum search problem is mapped to a time-optimal control problem. Resorting to Pontryagin's Minimum Principle we find that the time-optimal solution has the bang-singular-bang structure. This structure can be derived naturally, without integrating the differential equations, using the geometric control technique where Hamiltonians in the Schrödinger's equation are represented as vector fields. In view of optimal control, Grover's algorithm uses the bang-bang protocol to approximate the optimal protocol with a minimized number of bang-to-bang switchings to reduce the query complexity. Our work provides a concrete example how Pontryagin's Minimum Principle is connected to quantum computation, and offers insight into how a quantum algorithm can be designed.

quant-ph↗

arXiv2016

MPC on manifolds with an application to the control of spacecraft attitude on SO(3)

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.

math.OC↗