arXiv subjects

Thinh Nguyen

Publications and source records attributed to Thinh Nguyen.

39 records · Page 3Linked to original sources

arXiv2016

Flatness-based nonlinear control strategies for trajectory tracking of quadcopter systems

This paper proposes several nonlinear control strategies for trajectory tracking of a quadcopter system based on the property of differential flatness. Its originality is twofold. Firstly, it provides a flat output for the quadcopter dynamics capable of creating full flat parametrization of the states and inputs. Moreover, B-splines characterizations of the flat output and their properties allow for optimal trajectory generation subject to way-point constraints. Secondly, several control strategies based on computed torque control and feedback linearization are presented and compared. The advantages of flatness within each control strategy are analyzed and detailed through extensive simulation results.

eess.SY↗

arXiv2012

Stable Adiabatic Times for Markov Chains

In this paper we continue our work on adiabatic time of time-inhomogeneous Markov chains first introduced in Kovchegov (2010) and Bradford and Kovchegov (2011). Our study is an analog to the well-known Quantum Adiabatic (QA) theorem which characterizes the quantum adiabatic time for the evolution of a quantum system as a result of applying of a series of Hamilton operators, each is a linear combination of two given initial and final Hamilton operators, i.e. $\mathbf{H}(s) = (1-s)\mathbf{H_0} + s\mathbf{H_1}$. Informally, the quantum adiabatic time of a quantum system specifies the speed at which the Hamiltonian operators changes so that the ground state of the system at any time $s$ will always remain $ε$-close to that induced by the Hamilton operator $\mathbf{H}(s)$ at time $s$. Analogously, we derive a sufficient condition for the stable adiabatic time of a time-inhomogeneous Markov evolution specified by applying a series of transition probability matrices, each is a linear combination of two given irreducible and aperiodic transition probability matrices, i.e., $\mathbf{P_{t}} = (1-t)\mathbf{P_{0}} + t\mathbf{P_{1}}$. In particular we show that the stable adiabatic time $t_{sad}(\mathbf{P_{0}}, \mathbf{P_{1}}, ε) = O (t_{mix}^{4}(ε\slash 2) \slash ε^{3}), $ where $t_{mix}$ denotes the maximum mixing time over all $\mathbf{P_{t}}$ for $0 \leq t \leq 1$.

math.PR↗

arXiv2011

Framework for discrete-time quantum walks and a symmetric walk on a binary tree

We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2 on which this is based. The framework has no need for coin spaces, it imposes no constraints on the evolution operator other than unitarity, and is unifying of other approaches. As an example we construct a symmetric discrete-time quantum walk on the semi-infinite binary tree. The generating function of the amplitude at the root is computed in closed-form, as a function of time and the initial level n in the tree, and we find the asymptotic and a full numerical solution for the amplitude. It exhibits a sharp interference peak and a power law tail, as opposed to the exponentially decaying tail of a broadly peaked distribution of the classical symmetric random walk on a binary tree. The probability peak is orders of magnitude larger than it is for the classical walk (already at small n). The quantum walk shows a polynomial algorithmic speedup in n over the classical walk, which we conjecture to be of the order 2/3, based on strong trends in data.

quant-ph↗