arXiv subjects

Thang Nguyen

Publications and source records attributed to Thang Nguyen.

28 records · Page 2Linked to original sources

arXiv2018

Batch-normalized Recurrent Highway Networks

Gradient control plays an important role in feed-forward networks applied to various computer vision tasks. Previous work has shown that Recurrent Highway Networks minimize the problem of vanishing or exploding gradients. They achieve this by setting the eigenvalues of the temporal Jacobian to 1 across the time steps. In this work, batch normalized recurrent highway networks are proposed to control the gradient flow in an improved way for network convergence. Specifically, the introduced model can be formed by batch normalizing the inputs at each recurrence loop. The proposed model is tested on an image captioning task using MSCOCO dataset. Experimental results indicate that the batch normalized recurrent highway networks converge faster and performs better compared with the traditional LSTM and RHN based models.

cs.LG↗

arXiv2018

Rigidity of warped cones and coarse geometry of expanders

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian factors, then two such warped cones are quasi-isometric if and only if the actions are finite covers of conjugate actions. As a consequence, we produce continuous families of non-quasi-isometric expanders and superexpanders. The proof relies on the use of coarse topology for warped cones, such as a computation of their coarse fundamental groups.

math.MG↗

arXiv2017

State Estimation For An Agonistic-Antagonistic Muscle System

Research on assistive technology, rehabilitation, and prosthesis requires the understanding of human machine interaction, in which human muscular properties play a pivotal role. This paper studies a nonlinear agonistic-antagonistic muscle system based on the Hill muscle model. To investigate the characteristics of the muscle model, the problem of estimating the state variables and activation signals of the dual muscle system is considered. In this work, parameter uncertainty and unknown inputs are taken into account for the estimation problem. Three observers are presented: a high gain observer, a sliding mode observer, and an adaptive sliding mode observer. Theoretical analysis shows the convergence of the three observers. To facilitate numerical simulations, a backstepping controller is employed to drive the muscle system to track a desired trajectory. Numerical simulations reveal that the three observers are comparable and provide reliable estimates in noise free and noisy cases. The proposed schemes may serve as frameworks for estimation of complex multi-muscle systems, which could lead to intelligent exercise machines for adaptive training and rehabilitation, and adaptive prosthetics and exoskeletons.

eess.SY↗

arXiv2017

Quasi-isometric embeddings of non-uniform lattices

Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $Γ<G$ and $Λ< G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $Γ$ into $Λ$ is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of $SL(n,\mathbb Z)$ into $SL(n, \mathbb Z[i])$ is at bounded distance from a homomorphism. We also include a discussion of some cases when this result is not true for what turn out to be purely algebraic reasons.

math.GR↗

arXiv2017

Bounded Distributed Flocking Control of Nonholonomic Mobile Robots

There have been numerous studies on the problem of flocking control for multiagent systems whose simplified models are presented in terms of point-mass elements. Meanwhile, full dynamic models pose some challenging problems in addressing the flocking control problem of mobile robots due to their nonholonomic dynamic properties. Taking practical constraints into consideration, we propose a novel approach to distributed flocking control of nonholonomic mobile robots by bounded feedback. The flocking control objectives consist of velocity consensus, collision avoidance, and cohesion maintenance among mobile robots. A flocking control protocol which is based on the information of neighbor mobile robots is constructed. The theoretical analysis is conducted with the help of a Lyapunov-like function and graph theory. Simulation results are shown to demonstrate the efficacy of the proposed distributed flocking control scheme.

cs.RO↗

arXiv2017

Distributed Formation Control of Nonlonolomic Mobile Robots by Bounded Feedback in the Presence of Obstacles

The problem of distributed formation control of nonholonomic mobile robots is addressed in this paper, in which the robots are designed to track a formation. Collision avoidance among agents is guaranteed using a control law based on a repulsive force. In an uncertain environment where obstacles exist, the construction of repulsive force and rotational direction enables agents to avoid and pass the obstacles. The control inputs of each robot are designed to be bounded. Numerical simulations with different formations are implemented to demonstrate the efficacy of the proposed scheme.

cs.RO↗

arXiv2017

Hyperbolic rank rigidity for manifolds of $\frac14$-pinched negative curvature

A Riemannian manifold $M$ has higher hyperbolic rank if every geodesic has a perpendicular Jacobi field making sectional curvature -1 with the geodesic. If in addition, the sectional curvatures of $M$ lie in the interval $[-1,-\frac14]$, and $M$ is closed, we show that $M$ is a locally symmetric space of rank one. This partially extends work by Constantine using completely different methods. It is also a partial converse to Hamenstädt's hyperbolic rank rigidity result for sectional curvatures $\leq -1$, and complements well-known results on Euclidean and spherical rank rigidity.

math.DG↗

arXiv2017

Distributed Formation Control for Autonomous Robots in Dynamic Environments

In this paper, we propose a novel and distributed formation control method for autonomous robots to follow the desired formation while tracking a moving target in dynamic environments. In our approach, the desired formations, which include the virtual nodes arranged into specific shapes, are first generated. Then, autonomous robots are controlled by the proposed artificial force fields in order to converge to these virtual nodes without collisions. The stability analysis based on the Lyapunov approach is given. Moreover, a new combination of rotational force field and repulsive force field in designing an obstacle avoidance controller allows the robot to avoid and escape the convex and nonconvex obstacle shapes. The V-shape and circular shape formations with their advantages are utilized to test the effectiveness of the proposed method.

cs.RO↗

arXiv2014

A unified method for optimal arbitrary pole placement

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain. Lastly we compare the performance of our method against several others from the recent literature.

math.OC↗

arXiv2013

Robust pole placement with Moore's algorithm

We consider the classic problem of pole placement by state feedback. We adapt the Moore eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix, and introduce an unconstrained nonlinear optimization algorithm to obtain a gain matrix that will deliver robust pole placement. Numerical experiments indicate the algorithm's performance compares favorably against several other notable robust pole placement methods from the literature.

math.OC↗